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Praise for
出于对物理的热爱
For the Love of Physics
“引人入胜……这是一部令人愉悦的科学回忆录，同时也是一部令人难忘的物理学入门读物。”
“Fascinating. . . . A delightful scientific memoir combined with a memorable introduction to physics.”
—— 《科克斯书评》
—Kirkus Reviews
“麻省理工学院的莱温教授因其令人难忘的物理学讲座（包括现场讲座、麻省理工学院开放课程网站和YouTube上的讲座）而广受欢迎，这本节奏明快的自传兼物理学入门读物充分展现了他的坦率和生动的教学风格……令人愉悦……[本书]充满活力，应该会受到广大读者的喜爱。”
“MIT’s Lewin is deservedly popular for his memorable physics lectures (both live and on MIT’s OpenCourseWare website and YouTube), and this quick-paced autobiography-cum-physics intro fully captures his candor and lively teaching style . . . joyful . . . [this text] glows with energy and should please a wide range of readers.”
—— 《出版人周刊》（星级评论）
—Publishers Weekly (starred review)
“莱文或许是世界上唯一一位用鲜花来赞美麦克斯韦电磁场方程之美的物理学教授，他会把鲜花分发给欣喜若狂的学生们。成千上万曾亲身或在线聆听过他讲座的学生可以作证，这位课堂奇才将教科书上的公式化腐朽为神奇。莱文的非凡创造力熠熠生辉……这是一张通往冒险的通行证。”
“Lewin may be the only physics professor in the world who celebrates the beauty of Maxwell’s equations for electromagnetic fields by passing out flowers to his delighted students. As the hundreds of thousands of students who have witnessed his lectures in person or online can attest, this classroom wizard transforms textbook formulas into magic. Lewin’s rare creativity shines through . . . a passport to adventure.”
— 《书单》（星级评论）
—Booklist (starred review)
“在所有因YouTube而走红的人中——贾斯汀·比伯、婚礼入场舞者、拍摄双彩虹时失去理智的男子——没有谁比麻省理工学院物理学教授沃尔特·莱文更值得拥有这样的名气。这位教授的好奇心在他的新书《热爱物理：从彩虹的尽头到时间的边缘——一段探索物理奇观的旅程》中展现得淋漓尽致。为什么彩虹是弧线而不是直线？为什么我们通常只有在靠近北极或南极才能看到极光？如果你曾经对学习——或者重新学习——这些以及其他上百个引人入胜的问题的答案感兴趣，那么莱文的这本书就是为你准备的。”
“Of all the souls made famous by YouTube—Justin Bieber, those wedding entrance dancers, that guy who loses his mind while videotaping a double-rainbow—none is more deserving than MIT physics professor Walter Lewin. The professor’s sense of wonder is on full display in a new book: For the Love of Physics: From the End of the Rainbow to the Edge of Time—A Journey Through the Wonders of Physics. Why is a rainbow an arc and not a straight line? Why can we typically see auroras only if we’re close to the North or South Pole? If you’ve ever been interested in learning— or relearning—the answers to these and a hundred other fascinating questions, Lewin’s book is for you.”
—— 《波士顿环球报》
—The Boston Globe
“人人都知道暴风雨后会出现彩虹。但在莱文的新书中，他揭示了自然界更为奇特的彩虹：它们隐藏在海浪卷起的浪花中，车灯周围弥漫的雾气里，甚至漂浮在建筑工地上空的玻璃碎片中。在麻省理工学院教授本科物理三十余年后，莱文磨练出了一套清晰易懂、引人入胜的讲解方法，将物理学展现为一种揭示世界隐秘奇观的途径。本书风格奇特、生动有趣，又饱含真挚的情感，每一章都像是一幅生动的素描，描绘了一个主题——从牛顿定律到莱文在X射线天文学领域的开创性发现。莱文的创造力对学生和教育工作者都极具启发意义……贯穿全书的，是他那份令人着迷的好奇心。”
“Everyone knows that rainbows appear after a storm. But in his new book, Lewin reveals nature’s more unusual rainbows hiding in spray kicked up by ocean waves, in fog swirling around headlights, even in glass particles floating above construction sites. After more than thirty years of teaching undergraduate physics at MIT, Lewin has honed a toolbox of clear, engaging explanations that present physics as a way of uncovering the world’s hidden wonders. Quirky, playful, and brimming with earnestness, each chapter is a joyful sketch of a topic—from Newton’s laws to Lewin’s own pioneering discoveries in X-ray astronomy. Lewin’s creativity offers lessons both for students and for educators. . . . Throughout it all, his sense of wonder is infectious.”
—科学新闻
—Science News
“沃尔特·莱文对物理学的热情毫不掩饰，在这本色彩斑斓、带有浓厚自传色彩的科学之旅中，字里行间都闪耀着光芒。发现的兴奋之情极具感染力。”
“Walter Lewin’s unabashed passion for physics shines through on every page of this colorful, largely autobiographical tour of science. The excitement of discovery is infectious.”
——马里奥·利维奥，《黄金比例》 和《上帝是数学家吗？》的作者
—Mario Livio, author of The Golden Ratio and Is God a Mathematician?
“在这本有趣、引人入胜且通俗易懂的书中，课堂上的超级英雄沃尔特·莱文运用他的力量造福我们！作者们分享了学习的乐趣，让我们意识到世界是一个可以了解的地方。”
“In this fun, engaging, and accessible book, Walter Lewin, a superhero of the classroom, uses his powers for good—ours! The authors share the joy of learning that the world is a knowable place.”
——詹姆斯·卡卡利奥斯，教授，《超级英雄的物理学》 和《量子力学的奇妙故事》的作者
—James Kakalios, professor and author of The Physics of Superheroes and The Amazing Story of Quantum Mechanics
自由报
Free Press
西蒙与舒斯特公司旗下部门，地址：美洲大道1230号
A Division of Simon & Schuster, Inc. 1230 Avenue of the Americas
纽约, NY 10020
www.SimonandSchuster.com
New York, NY 10020
www.SimonandSchuster.com
版权所有 © 2011 Walter Lewin 和 Warren Goldstein
Copyright © 2011 by Walter Lewin and Warren Goldstein
保留所有权利，包括以任何形式复制本书或其任何部分的权利。如需了解更多信息，请联系自由出版社附属版权部门，地址：1230 Avenue of the Americas, New York, NY 10020。
All rights reserved, including the right to reproduce this book or portions thereof in any form whatsoever. For information address Free Press Subsidiary Rights Department, 1230 Avenue of the Americas, New York, NY 10020.
2011年5月，自由出版社首版精装本
First Free Press hardcover edition May 2011
FREE PRESS 和版权标识是 Simon & Schuster, Inc. 的商标。
FREE PRESS and colophon are trademarks of Simon & Schuster, Inc.
西蒙与舒斯特演讲局可以安排作者出席您的现场活动。如需了解更多信息或预订活动，请致电西蒙与舒斯特演讲局 1-866-248-3049 或访问我们的网站www.simonspeakers.com。
The Simon & Schuster Speakers Bureau can bring authors to your live event. For more information or to book an event contact the Simon & Schuster Speakers Bureau at 1-866-248-3049 or visit our website at www.simonspeakers.com.
书籍设计：Ellen R. Sasahara
Book design by Ellen R. Sasahara
美国制造
Manufactured in the United States of America
1 3 5 7 9 10 8 6 4 2
1 3 5 7 9 10 8 6 4 2
美国国会图书馆出版物编目数据
Library of Congress Cataloging-in-Publication Data
莱文，沃尔特·HG
Lewin, Walter H. G.
出于对物理的热爱：从彩虹的尽头到时间的边缘——一段探索物理奇迹的旅程 / 作者：沃尔特·莱文和沃伦·戈德斯坦。
For the love of physics : from the end of the rainbow to the edge of time—a journey through the wonders of physics / by Walter Lewin with Warren Goldstein.
厘米
p. cm.
1. 莱温，沃尔特·H·G 2. 物理学家——马萨诸塞州——传记。3. 大学教师——马萨诸塞州——传记。4. 物理学——研究与教学——荷兰。5. 物理学——研究与教学——马萨诸塞州。I. 戈尔茨坦，沃伦·杰伊。II. 标题。
1. Lewin, Walter H. G. 2. Physicists—Massachusetts—Biography. 3. College teachers—Massachusetts—Biography. 4. Physics—Study and teaching—Netherlands. 5. Physics—Study and teaching—Massachusetts. I. Goldstein, Warren Jay. II. Title.
QC16.L485A3 2011
QC16.L485A3 2011
530.092—dc22
530.092—dc22
[B] 2010047737
[B] 2010047737
ISBN 978-1-4391-0827-7
ISBN 978-1-4391-0827-7
ISBN 978-1-4391-2354-6（电子书）
ISBN 978-1-4391-2354-6 (ebook)
内容
CONTENTS
1. From the Nucleus to Deep Space
2. Measurements, Uncertainties, and the Stars
4. The Magic of Drinking with a Straw
5. Over and Under—Outside and Inside—the Rainbow
6. The Harmonies of Strings and Winds
9. Energy Conservation—Plus ça change…
11. X-ray Ballooning, the Early Days
介绍
INTRODUCTION
这位教授身高六英尺二英寸，身材精瘦，身穿一件看似蓝色的工作衬衫，袖子卷到手肘，下身是卡其色工装裤，脚蹬凉鞋和白袜子。他踱步在阶梯教室前，一边高声朗诵，一边比划手势，偶尔会在一排长长的黑板和一张齐腰高的实验桌之间停下来强调重点。他面前的四百把椅子呈倾斜状，学生们坐在那里，不时挪动身子，但目光始终紧盯着教授。教授给人的感觉是，他体内仿佛涌动着一股强大的能量，难以抑制。他额头高耸，一头蓬乱的灰发，戴着眼镜，带着一丝难以辨认的欧洲口音，让人想起电影《回到未来》中克里斯托弗·劳埃德饰演的布朗博士——那位充满激情、超凡脱俗、略带疯狂的科学家兼发明家。
Six feet two and lean, wearing what looks like a blue work shirt, sleeves rolled to the elbows, khaki cargo pants, sandals and white socks, the professor strides back and forth at the front of his lecture hall, declaiming, gesturing, occasionally stopping for emphasis between a long series of blackboards and a thigh-high lab table. Four hundred chairs slope upward in front of him, occupied by students who shift in their seats but keep their eyes glued to their professor, who gives the impression that he is barely containing some powerful energy coursing through his body. With his high forehead, shock of unruly grey hair, glasses, and the trace of some unidentifiable European accent, he gives off a hint of Christopher Lloyd’s Doc Brown in the movie Back to the Future—the intense, otherworldly, slightly mad scientist-inventor.
但这可不是布朗博士的车库——这是麻省理工学院，美国乃至全世界首屈一指的科学与工程大学，而正在黑板前讲课的是沃尔特·H·G·莱文教授。他停下脚步，转向学生。“现在。测量中最重要的一点，也是所有大学物理教材都忽略的一点，”他张开双臂，手指分开，“就是测量的不确定性。”他停顿了一下，向前迈了一步，给学生们一些思考的时间，然后又停了下来：“任何你在不知道不确定性的情况下进行的测量，都是不准确的。”毫无意义。 ”说着，双手猛地分开，在空中挥舞，以示强调。又是一阵停顿。
But this is not Doc Brown’s garage—it’s the Massachusetts Institute of Technology, the preeminent science and engineering university in the United States, perhaps even the world, and lecturing at the blackboard is Professor Walter H. G. Lewin. He halts his stride and turns to the class. “Now. All important in making measurements, which is always ignored in every college physics book”—he throws his arms wide, fingers spread—“is the uncertainty in your measurements.” He pauses, takes a step, giving them time to consider, and stops again: “Any measurement that you make without knowledge of the uncertainty is meaningless.” And the hands fly apart, chopping the air for emphasis. Another pause.
“我再说一遍。今晚凌晨三点你们醒来的时候，一定要听清楚。”他用两根食指按着太阳穴，扭动着，假装要钻进自己的脑子里。“任何你不知道其不确定性的测量都是毫无意义的。 ”学生们目不转睛地盯着他，全神贯注。
“I will repeat this. I want you to hear it tonight at three o’clock in the morning when you wake up.” He is holding both index fingers to his temples, twisting them, pretending to bore into his brain. “Any measurement that you make without knowledge of its uncertainty is completely meaningless.” The students stare at him, utterly rapt.
我们现在才上了11分钟物理8.01的第一节课，这是世界上最著名的大学物理入门课程。
We’re just eleven minutes into the first class of Physics 8.01, the most famous introductory college physics course in the world.
2007年12月， 《纽约时报》头版刊登了一篇关于沃尔特·莱文的报道，称他为麻省理工学院的“网络明星”。报道重点介绍了莱文在麻省理工学院开放课程网站、YouTube、iTunes U和Academic Earth等平台上发布的物理学讲座。莱文的讲座是麻省理工学院最早上传到互联网的讲座之一，事实证明，这一举措非常成功。这些讲座广受欢迎。这94节课——分为三门完整课程和七节独立课程——每天吸引约3000名观众，每年点击量达100万次。其中不乏比尔·盖茨的身影。据他写给莱文的信件（当然是手写的！）显示，盖茨已经观看了全部8.01“经典力学”和8.02“电磁学”课程，并表示期待接下来的8.03“振动与波动”课程。
The New York Times ran a front-page piece on Walter Lewin as an MIT “webstar” in December 2007, featuring his physics lectures available on the MIT OpenCourseWare site, as well as on YouTube, iTunes U, and Academic Earth. Lewin’s were among the first lectures that MIT posted on the Internet, and it paid off for MIT. They have been exceptionally popular. The ninety-four lectures—in three full courses, plus seven stand-alones—garner about three thousand viewers per day, a million hits a year. Those include quite a few visits from none other than Bill Gates, who’s watched all of courses 8.01, Classical Mechanics, and 8.02, Electricity and Magnetism, according to letters (snail mail!) he’s sent Walter, reporting that he was looking forward to moving on to 8.03, Vibrations and Waves.
“您改变了我的人生”，这是莱文每天都会收到的来自世界各地、各个年龄段的邮件中常见的标题。来自圣地亚哥的花店老板史蒂夫写道：“我走路都轻快了，我用物理学的视角看待生活。”突尼斯工程预科学校的学生穆罕默德写道：“不幸的是，在我的国家，我的教授们并不像您那样欣赏物理学的美，我因此深受其害。他们只想让我们学会如何解答‘典型’的习题以通过考试，他们的视野仅限于此。”已经获得两个美国硕士学位的伊朗学生赛义德写道：“直到我听了您的物理课，我才真正体会到生活的乐趣。莱文教授，您真的改变了我的人生。您的教学方式物超所值，远超学费。”有些老师（并非所有老师）简直就是一群罪犯。教错书是死罪。”或者来自印度的西达尔特说：“我能感受到那些方程式之外的物理意义。你的学生会永远记住你，就像我会永远记住你一样——你是一位非常非常优秀的老师，你让生活和学习变得比我想象的还要有趣。”
“You have changed my life,” runs a common subject line in the emails Lewin receives every day from people of all ages and from all over the world. Steve, a florist from San Diego, wrote, “I walk with a new spring in my step and I look at life through physics-colored eyes.” Mohamed, an engineering prep school student in Tunisia wrote, “Unfortunately, here in my country my professors don’t see any beauty in physics as you do see, and I’ve suffered a lot from this. They just want us to learn how to solve ‘typical’ exercises to succeed in the exam, they don’t look beyond that tiny horizon.” Seyed, an Iranian who had already earned a couple of American master’s degrees, writes, “I never really enjoy of life until I have watched you teach physics. Professor Lewin you have changed my life Indeed. The way you teach it is worth 10 times the tuition, and make SOME not all other teachers bunch of criminals. It is CAPITAL CRIME to teach bad.” Or Siddharth from India: “I could feel Physics beyond those equations. Your students will always remember you as I will always remember you—as a very-very fine teacher who made life and learning more interesting than I thought was possible.”
穆罕默德热情地引用了莱文在物理8.01课程的最后一讲，并表示赞同：“或许你们会永远记得，在我的讲课中，物理学可以非常精彩、非常美妙，它无处不在，无时无刻不在我们身边，只要你们学会观察和欣赏它的美。”另一位粉丝玛乔丽写道：“我尽可能多地观看你的节目，有时一周五次。我被你的个性、你的幽默感，尤其是你化繁为简的能力深深吸引。我高中时讨厌物理，但你让我爱上了它。”
Mohamed enthusiastically quotes Lewin’s final lecture in Physics 8.01 with approval: “Perhaps you will always remember from my lectures that physics can be very exciting and beautiful and it’s everywhere around us, all the time, if only you have learned to see it and appreciate its beauty.” Marjory, another fan, wrote, “I watch you as often as I can; sometimes five times per week. I am fascinated by your personality, your sense of humor, and above all by your ability to simplify matters. I hated physics in high school, but you made me love it.”
莱文每周都会收到几十封这样的电子邮件，而且他每封都会回复。
Lewin receives dozens of such emails every week, and he answers each one.
沃尔特·莱文在讲解物理学的奇妙之处时，总能创造出令人着迷的魔力。他的秘诀是什么呢？“我把人们带入他们自己的世界，”他说，“他们生活的世界，他们熟悉的世界，但他们还没有像物理学家那样去理解它。如果我讲到水波，我会让他们在浴缸里做一些实验；他们能感同身受。他们也能理解彩虹。这就是我热爱物理学的原因之一：你可以解释任何事物。这对他们和我来说都是一次美妙的体验。我让他们爱上物理！有时，当我的学生真正投入其中时，课堂就像一场场精彩的演出。”
Walter Lewin creates magic when he introduces the wonders of physics. What’s his secret? “I introduce people to their own world,” he says, “the world they live in and are familiar with, but don’t approach like a physicist—yet. If I talk about waves on water, I ask them to do certain experiments in their bathtubs; they can relate to that. They can relate to rainbows. That’s one of the things I love about physics: you get to explain anything. And that can be a wonderful experience—for them and for me. I make them love physics! Sometimes, when my students get really engaged, the classes almost feel like happenings.”
他可能正站在十六英尺高的梯子顶端，用一根长长的、像蛇一样的实验室软管吸管，从地上的烧杯里吸吮蔓越莓汁。或者，他可能正冒着受伤的风险，把头伸向一个虽小但威力十足的铁球，铁球会摆动到离他下巴只有几毫米的地方。他可能正用步枪向两个装满水的油漆罐射击，或者用一个叫做范德格拉夫起电机的巨型装置——就像科幻电影里疯狂科学家实验室里的东西——给自己施加30万伏的电压，让他原本就蓬乱的头发从头骨上直直地竖起来。他使用他把自己的身体当作实验器材。正如他常说的，“毕竟，科学需要牺牲。” 在一次演示中——本书封面照片就记录了这一幕——他坐在一个极其不舒服的金属球上，这个金属球悬挂在从讲堂天花板垂下的绳子末端（他称之为“所有摆锤之母”），随着他来回摆动，而他的学生们则齐声喊出摆动的次数。这一切都是为了证明，摆锤在任何给定时间内摆动的次数与它末端的重物无关。
He might be perched at the top of a sixteen-foot ladder sucking cranberry juice out of a beaker on the floor with a long snaking straw made out of lab tubing. Or he could be courting serious injury by putting his head in the path of a small but quite powerful wrecking ball that swings to within millimeters of his chin. He might be firing a rifle into two paint cans filled with water, or charging himself with 300,000 volts of electricity with a large contraption called a Van de Graaff generator—like something out of a mad scientist’s laboratory in a science fiction movie—so that his already wild hair stands straight out from his skull. He uses his body as a piece of experimental equipment. As he says often, “Science requires sacrifices, after all.” In one demonstration—captured in the photo on the jacket of this book—he sits on an extremely uncomfortable metal ball at the end of a rope suspended from the lecture hall’s ceiling (what he calls the mother of all pendulums) and swings back and forth while his students chant the number of swings, all to prove that the number of swings a pendulum makes in any given time is independent of the weight at its end.
他的儿子伊曼纽尔（查克）·莱文曾旁听过他的一些讲座，并回忆道：“我曾亲眼看到他吸入氦气来改变嗓音。为了达到理想的效果——细节决定成败——他通常会吸到几乎晕倒的程度。”莱文是一位技艺精湛的黑板艺术家，他能信手拈来地绘制几何图形、矢量、图表、天文现象和动物。他绘制虚线的方法深深吸引了几位学生，他们甚至制作了一段名为“沃尔特·莱文的一些最佳线条”的趣味YouTube视频，视频内容仅仅是莱文在8.01课程中于不同黑板上绘制他标志性虚线的讲座片段。（您可以在这里观看：www.youtube.com/watch? v=raurl4s0pjU 。）
His son, Emanuel (Chuck) Lewin, has attended some of these lectures and recounts, “I saw him once inhale helium to change his voice. To get the effect right—the devil is in the details—he typically gets pretty close to the point of fainting.” An accomplished artist of the blackboard, Lewin draws geometrical figures, vectors, graphs, astronomical phenomena, and animals with abandon. His method of drawing dotted lines so entranced several students that they produced a funny YouTube video titled “Some of Walter Lewin’s Best Lines,” consisting simply of lecture excerpts showing Lewin drawing his famous dotted lines on different blackboards during his 8.01 lectures. (You can watch it here: www.youtube.com/watch?v=raurl4s0pjU.)
莱文气场强大，魅力十足，同时也是个名副其实的怪人：他古怪另类，痴迷于物理学。他的钱包里总是装着两个叫做偏振器的装置，这样他就能随时查看任何光源，比如蓝天、彩虹或窗户上的反射光，是否是偏振光，而且他身边的人也能看到。
A commanding, charismatic presence, Lewin is a genuine eccentric: quirky and physics obsessed. He carries two devices called polarizers in his wallet at all times, so that at a moment’s notice he can see if any source of light, such as the blue sky, a rainbow, or reflections off windows, is polarized, and whoever he might be with can see it too.
那他上课穿的那些蓝色工作衬衫呢？原来根本不是工作衬衫。莱文每隔几年都会从香港的一位裁缝那里订购一打，都是根据他的要求，用高档棉布量身定制的。左侧的超大口袋是莱文自己设计的，用来装他的日历。这里没有口袋保护套——这位物理学家、表演家兼教师对穿着打扮一丝不苟——这不禁让人好奇，他为什么会戴着一枚大学教授佩戴过的最奇特的胸针：一个塑料煎蛋。“总比蛋掉在脸上强，”他说。
What about those blue work shirts he wears to class? Not work shirts at all, it turns out. Lewin orders them, custom made to his specifications, of high-grade cotton, a dozen at a time every few years, from a tailor in Hong Kong. The oversize pocket on the left side Lewin designed to accommodate his calendar. No pocket protectors here—this physicist-performer-teacher is a man of meticulous fashion—which makes a person wonder why he appears to be wearing the oddest brooch ever worn by a university professor: a plastic fried egg. “Better,” he says, “to have egg on my shirt than on my face.”
他左手上那枚超大的粉色亚克力戒指是怎么回事？还有，他肚脐位置衬衫上那个银色的东西又是什么？他总是偷偷地看它。
What is that oversize pink Lucite ring doing on his left hand? And what is that silvery thing pinching his shirt right at belly-button level, which he keeps sneaking looks at?
每天早上，莱文在穿戴时，都会从四十枚戒指、三十五枚胸针以及数十条手链和项链中挑选。他的品味包罗万象，从风格各异的（肯尼亚串珠手链、一条由大块琥珀串成的项链、塑料水果胸针）到古董（一条厚重的土库曼银质手镯），再到设计师和艺术家创作的珠宝，以及一些简单却又滑稽古怪的（一条用毛毡甘草糖串成的项链）。“学生们开始注意到这一点，”他说，“所以我开始每节课都佩戴不同的饰品。尤其是给孩子们演讲的时候，他们很喜欢。”
Every morning as Lewin dresses, he has the choice of forty rings and thirty-five brooches, as well as dozens of bracelets and necklaces. His taste runs from the eclectic (Kenyan beaded bracelets, a necklace of large amber pieces, plastic fruit brooches) to the antique (a heavy silver Turkmen cuff bracelet) to designer and artist-created jewelry, to the simply and hilariously outrageous (a necklace of felt licorice candies). “The students started noticing,” he says, “so I began wearing a different piece every lecture. And especially when I give talks to kids. They love it.”
他衬衫上别着的那个看起来像超大号领带夹的东西？那是一款特制的腕表（一位艺术家朋友送的），表盘是倒置的，这样莱文就可以低头看衬衫上的时间了。
And that thing clipped to his shirt that looks like an oversize tie clip? It’s a specially designed watch (the gift of an artist friend) with the face upside down, so Lewin can look down at his shirt and keep track of time.
有时，在旁人看来，莱文似乎心不在焉，或许是一位典型的健忘教授。但实际上，他通常都在全神贯注地思考物理学的某个方面。正如他的妻子苏珊·考夫曼最近回忆的那样：“我们去纽约的时候，我总是开车。但最近我拿出了一张地图，我也不知道为什么，但我注意到地图上各州的边缘都写满了方程式。那些边缘的文字是他上次讲课时写的，当时我们开车，他觉得很无聊。物理始终萦绕在他的心头。他的学生和学校一天24小时都与他同在。”
It sometimes seems to others that Lewin is distracted, perhaps a classic absentminded professor. But in reality, he is usually deeply engaged in thinking about some aspect of physics. As his wife Susan Kaufman recently recalled, “When we go to New York I always drive. But recently I took this map out, I’m not sure why, but when I did I noticed there were equations all over the margins of the states. Those margins were done when he was last lecturing, and he was bored when we were driving. Physics was always on his mind. His students and school were with him twenty-four hours a day.”
据他的老朋友、建筑史学家南希·斯蒂伯 (Nancy Stieber) 所说，莱文最引人注目的性格特点或许是“他兴趣的专注力极其强烈。他似乎总是全身心投入到他选择参与的任何事情中，并排除掉世间90%的事物。凭借这种激光般的专注力，他剔除了对他而言无关紧要的东西，从而达到一种如此强烈的投入状态，并由此产生了一种非凡的生活乐趣。 ”
Perhaps most striking of all about Lewin’s personality, according to his longtime friend the architectural historian Nancy Stieber, is “the laser-sharp intensity of his interest. He seems always to be maximally engaged in whatever he chooses to be involved in, and eliminates 90 percent of the world. With that laserlike focus, he eliminates what’s inessential to him, getting to a form of engagement that is so intense, it produces a remarkable joie de vivre.”
莱文是个完美主义者；他对细节有着近乎狂热的执着。他不仅是世界顶尖的物理学教师；他还是X射线天文学领域的先驱，并花了二十年时间进行研究和建设。他利用超灵敏的设备对亚原子和天文现象进行测试和观测，这些设备能够以惊人的精度测量X射线。他发射了巨大而极其精密的气球，掠过地球大气层的上缘，开始揭示一系列奇特的天文现象，例如X射线暴。他和该领域的同事们的发现有助于揭开恒星在超新星爆发中死亡的神秘面纱，并证实黑洞确实存在。
Lewin is a perfectionist; he has an almost fanatical obsession with detail. He is not only the world’s premier physics teacher; he was also a pioneer in the field of X-ray astronomy, and he spent two decades building, testing, and observing subatomic and astronomical phenomena with ultrasensitive equipment designed to measure X-rays to a remarkable degree of accuracy. Launching enormous and extremely delicate balloons that skimmed the upper limit of Earth’s atmosphere, he began to uncover an exotic menagerie of astronomical phenomena, such as X-ray bursters. The discoveries he and his colleagues in the field made helped to demystify the nature of the death of stars in massive supernova explosions and to verify that black holes really do exist.
他学会了反复试验——这不仅解释了他作为一名观测天体物理学家的成功，也解释了他为何能如此清晰地揭示牛顿定律的雄伟之处，小提琴的琴弦为何能发出如此优美的共鸣音，以及为什么你在乘坐电梯时体重会短暂地增减。
He learned to test, and test, and test again—which not only accounts for his success as an observational astrophysicist, but also for the remarkable clarity he brings to revealing the majesty of Newton’s laws, why the strings of a violin produce such beautifully resonant notes, and why you lose and gain weight, be it only very briefly, when you ride in an elevator.
为了准备讲课，他总会在空教室里至少练习三次，最后一次练习是在讲课当天早上五点。“他的讲课之所以有效，”曾与他一起上课的天体物理学家大卫·普利说，“是因为他投入的时间。”
For his lectures, he always practiced at least three times in an empty classroom, with the last rehearsal being at five a.m. on lecture day. “What makes his lectures work,” says astrophysicist David Pooley, a former student who worked with him in the classroom, “is the time he puts into them.”
2002年，麻省理工学院物理系提名莱文角逐一项享有盛誉的教学奖时，他的许多同事都特别强调了他身上的这些特质。史蒂文·利布（Steven Leeb）对莱文教授的物理学习经历有着最生动的描述。利布现任麻省理工学院电磁与电子系统实验室的电气工程与计算机科学教授，他曾在1984年选修过莱文教授的电磁学课程。“他一登台就气势磅礴，”利布回忆道，“一下子就抓住了我们的大脑，带我们体验了一场电磁学的过山车之旅，至今我仍能感受到那种震撼。他是一位课堂天才，拥有无与伦比的创造力，总能找到通俗易懂的讲解方法。”
When MIT’s Physics Department nominated Lewin for a prestigious teaching award in 2002, a number of his colleagues zeroed in on these exact qualities. One of the most evocative descriptions of the experience of learning physics from Lewin is from Steven Leeb, now a professor of electrical engineering and computer science at MIT’s Laboratory for Electromagnetic and Electronic Systems, who took his Electricity and Magnetism course in 1984. “He exploded onto the stage,” Leeb recalls, “seized us by the brains, and took off on a roller-coaster ride of electromagnetics that I can still feel on the back of my neck. He is a genius in the classroom with an unmatched resourcefulness for finding ways to make concepts plain.”
罗伯特·赫尔西泽是莱文在物理系的同事，他曾试图将莱文的一些课堂演示剪辑成视频，制作成一部集锦影片供其他大学观看。但他发现这项任务根本无法完成。“这些演示与整个发展过程融合得如此完美。”这些想法，包括铺垫和结局，使得演示的开始和结束时间并不明确。在我看来，沃尔特的表达方式非常丰富，无法被简单地分割成几小块。
Robert Hulsizer, one of Lewin’s Physics Department colleagues, tried to excerpt some of Lewin’s in-class demonstrations on video to make a kind of highlight film for other universities. He found the task impossible. “The demonstrations were so well woven into the development of the ideas, including a buildup and denouement, that there was no clear time when the demonstration started and when it finished. To my mind, Walter had a richness of presentation that could not be sliced into bites.”
沃尔特·莱温介绍物理学奇妙之处的方式令人兴奋之处在于，他传递了对我们世界所有奇妙之处的巨大喜悦。他的儿子查克深情地回忆起父亲如何尽心尽力地将快乐传递给他们兄弟姐妹：“他有一种神奇的能力，能让你看到事物的美好，让你为之倾倒，在你心中激起喜悦、惊叹和兴奋的情绪。我说的是他创造的那些令人难以置信的美好瞬间，你会感到无比幸福，因为活着就是为了他，为了他所创造的一切。有一次我们去缅因州度假。我记得那天天气不太好，我们几个孩子像其他孩子一样，无聊地待在一起。不知怎么的，我父亲拿了个小球，自发地玩起了这个奇特的小游戏，没过多久，隔壁海滩的几个孩子也过来了，突然间，我们四个、五个、六个人一起扔球、接球，欢声笑语不断。我记得当时我兴奋极了，无比快乐。回首往事，想想是什么激励着我的人生，那就是那些纯粹的快乐时刻，那些对美好生活的憧憬，那些对生活无限可能的感悟。”等等——这是我从我父亲那里遗传来的。
The thrill of Walter Lewin’s approach to introducing the wonders of physics is the great joy he conveys about all the wonders of our world. His son Chuck fondly recalls his father’s devotion to imparting that sense of joy to him and his siblings: “He has this ability to get you to see things and to be overwhelmed by how beautiful they are, to stir the pot in you of joy and amazement and excitement. I’m talking about little unbelievable windows he was at the center of, you felt so happy to be alive, in his presence, in this event that he created. We were on vacation in Maine once. It wasn’t great weather, I recall, and we kids were just hanging out, the way kids do, bored. Somehow my father got a little ball and spontaneously created this strange little game, and in a minute some of the other beach kids from next door came over, and suddenly there were four, five, six of us throwing, catching, and laughing. I remember being so utterly excited and joyful. If I look back and think about what’s motivated me in my life, having those moments of pure joy, having a vision of how good life can be, a sense of what life can hold—I’ve gotten that from my father.”
沃尔特过去常常在冬天组织孩子们玩一个游戏，测试纸飞机的空气动力学性能——把纸飞机扔进家里的大客厅壁炉里。“令我母亲惊恐的是，”查克回忆说，“我们竟然能把它们从火里捞出来——我们决心下次一定要赢！”
Walter used to organize his children to play a game in the winter, testing the aerodynamic quality of paper airplanes—by flying them into the family’s big open living room fireplace. “To my mother’s horror,” Chuck recalled, “we would recover them from the fire—we were determined to win the competition the next time round!”
每当有客人来吃晚饭，沃尔特就会主持“登月”游戏。查克回忆说：“我们会把灯光调暗，用拳头敲桌子，发出类似鼓声的轰鸣，模拟火箭发射的声音。有些孩子甚至会钻到桌子底下敲。然后，当我们‘到达太空’时，我们就停止敲击；一旦我们‘降落’在月球上，我们所有人都会在客厅里走来走去，假装自己处于低重力状态，做出各种夸张的举动。”一步一步地走下去。与此同时，客人们肯定在想：“这些人疯了吧！”但对我们孩子来说，这简直太棒了！我们要去月球了！
When guests came for dinner, Walter would preside over the game of Going to the Moon. As Chuck remembers it, “We would dim the lights, pound our fists on the table making a drumroll kind of sound, simulating the noise of a rocket launch. Some of the kids would even go under the table and pound. Then, as we reached space, we stopped the pounding, and once we landed on the Moon, all of us would walk around the living room pretending to be in very low gravity, taking crazy exaggerated steps. Meanwhile, the guests must have been thinking, ‘These people are nuts!’ But for us kids, it was fantastic! Going to the Moon!”
自半个多世纪前沃尔特·莱温踏入教室的那一刻起，他就带领学生们探索着未知的领域。他始终被自然界的神秘与美丽所深深吸引——从彩虹到中子星，从老鼠的股骨到音乐的旋律——同时也为科学家和艺术家们为解释、诠释和展现这个世界所做的努力而倾注心力。沃尔特·莱温是当今在世的最热情、最专注、最技艺精湛的科学向导之一。在接下来的章节中，你将感受到他对物理学的热情、专注和精湛技艺，他将向你揭示他毕生对物理学的热爱，并与你分享。祝你阅读愉快！
Walter Lewin has been taking students to the Moon since he first walked into a classroom more than a half century ago. Perpetually entranced by the mystery and beauty of the natural world—from rainbows to neutron stars, from the femur of a mouse to the sounds of music—and by the efforts of scientists and artists to explain, interpret, and represent this world, Walter Lewin is one of the most passionate, devoted, and skillful scientific guides to that world now alive. In the chapters that follow you will be able to experience that passion, devotion, and skill as he uncovers his lifelong love of physics and shares it with you. Enjoy the journey!
——沃伦·戈德斯坦
—Warren Goldstein
第一章
CHAPTER 1
从原子核到深空
From the Nucleus to Deep Space
真是不可思议。我外公是个文盲，只是个清洁工。两代之后，我成了麻省理工学院的正教授。我非常感谢荷兰的教育体系。我在荷兰代尔夫特理工大学读研究生，可谓一举三得。
It’s amazing, really. My mother’s father was illiterate, a custodian. Two generations later I’m a full professor at MIT. I owe a lot to the Dutch educational system. I went to graduate school at the Delft University of Technology in the Netherlands, and killed three birds with one stone.
从一开始，我就开始教物理。为了支付学费，我不得不向荷兰政府贷款。如果我全职教书，每周至少20小时，政府每年会免除我五分之一的贷款。教书的另一个好处是不用服兵役。军队对我来说简直是灾难，糟糕透了。我天生就对权威反感——这完全是我的性格使然——我知道自己最终会变成一个只会顶嘴、干些脏活累活的家伙。所以，我在鹿特丹的黎巴嫩中学全职教数学和物理，每周22个课时，学生都是十六七岁的孩子。我既不用服兵役，不用偿还贷款，还能同时攻读博士学位。
Right from the start, I began teaching physics. To pay for school I had to take out a loan from the Dutch government, and if I taught full time, at least twenty hours a week, each year the government would forgive one-fifth of my loan. Another advantage of teaching was that I wouldn’t have to serve in the army. The military would have been the worst, an absolute disaster for me. I’m allergic to all forms of authority—it’s just in my personality—and I knew I would have ended up mouthing off and scrubbing floors. So I taught math and physics full time, twenty-two contact hours per week, at the Libanon Lyceum in Rotterdam, to sixteen-and seventeen-year-olds. I avoided the army, did not have to pay back my loan, and was getting my PhD, all at the same time.
我还学会了如何教书。对我来说，教高中生，能够以积极的方式改变年轻人的想法，这令人兴奋。我总是努力让课堂既有趣又轻松愉快。尽管学校本身管理非常严格，但学生们却很顽劣。教室门上方有横梁窗，一位校长有时会爬上椅子，透过横梁窗偷窥老师们。你敢相信吗？
I also learned to teach. For me, teaching high school students, being able to change the minds of young people in a positive way, that was thrilling. I always tried to make classes interesting but also fun for the students, even though the school itself was quite strict. The classroom doors had transom windows at the top, and one of the headmasters would sometimes climb up on a chair and spy on teachers through the transom. Can you believe it?
我当时并没有被学校文化所束缚，而且正值研究生阶段，我热情高涨。我的目标是将这份热情传递给我的学生，帮助他们以全新的视角看待周围的世界之美，改变他们，让他们也感受到物理世界的魅力，并理解物理无处不在，渗透在我们生活的方方面面。我发现，重要的不是你讲授了什么，而是你发现了什么。课堂上讲授知识可能会枯燥乏味，学生们也会有这种感觉。而揭示物理定律，让他们透过公式看到本质，则能展现发现的过程，其中充满了新鲜感和兴奋感，学生们会乐于参与其中。
I wasn’t caught up in the school culture, and being in graduate school, I was boiling over with enthusiasm. My goal was to impart that enthusiasm to my students, to help them see the beauty of the world all around them in a new way, to change them so that they would see the world of physics as beautiful, and would understand that physics is everywhere, that it permeates our lives. What counts, I found, is not what you cover, but what you uncover. Covering subjects in a class can be a boring exercise, and students feel it. Uncovering the laws of physics and making them see through the equations, on the other hand, demonstrates the process of discovery, with all its newness and excitement, and students love being part of it.
我也曾在课堂之外以另一种方式体验过这种经历。学校每年都会组织一次为期一周的假期，由一位老师带领孩子们前往一个相当偏远且原始的露营地。我和妻子惠伯莎参加过一次，非常喜欢。我们一起做饭，睡在帐篷里。由于远离城市灯光，我们半夜把孩子们叫醒，给他们喝热巧克力，然后带他们去看星星。我们一起辨认星座和行星，孩子们还亲眼目睹了银河的壮丽景象。
I got to do this also in a different way far outside the classroom. Every year the school sponsored a week-long vacation when a teacher would take the kids on a trip to a fairly remote and primitive campsite. My wife, Huibertha, and I did it once and loved it. We all cooked together and slept in tents. Then, since we were so far from city lights, we woke all the kids up in the middle of one night, gave them hot chocolate, and took them out to look at the stars. We identified constellations and planets and they got to see the Milky Way in its full glory.
我当时既没有学习也没有教授天体物理学——事实上，我当时正在设计实验来探测宇宙中一些最小的粒子——但我一直对天文学着迷。事实上，几乎每个物理学家都热爱天文学。我认识的许多物理学家在高中时就自己组装过望远镜。我的老朋友兼麻省理工学院同事乔治·克拉克在高中时就打磨抛光了一面6英寸的望远镜镜片。为什么物理学家如此热爱天文学呢？一方面，物理学的许多进步——例如轨道运动理论——都源于天文学问题、观测和理论。此外，天文学是物理学，只不过它以更广阔的视角展现在夜空中：日食、彗星、流星、球状星团、中子星、伽马射线暴、喷流、行星状星云、超新星、星系团、黑洞。
I wasn’t studying or even teaching astrophysics—in fact, I was designing experiments to detect some of the smallest particles in the universe—but I’d always been fascinated by astronomy. The truth is that just about every physicist who walks the Earth has a love for astronomy. Many physicists I know built their own telescopes when they were in high school. My longtime friend and MIT colleague George Clark ground and polished a 6-inch mirror for a telescope when he was in high school. Why do physicists love astronomy so much? For one thing, many advances in physics—theories of orbital motion, for instance—have resulted from astronomical questions, observations, and theories. But also, astronomy is physics, writ large across the night sky: eclipses, comets, shooting stars, globular clusters, neutron stars, gamma-ray bursts, jets, planetary nebulae, supernovae, clusters of galaxies, black holes.
抬头看看天空，问问自己一些显而易见的问题：为什么天空是蓝色的？为什么日落是红色的？为什么云是白色的？物理学可以解答这些问题！太阳光由彩虹的所有颜色组成。但是，当它穿过大气层时，会被空气分子和非常微小的尘埃颗粒（远小于微米，微米是1/250,000英寸）散射到各个方向。这被称为瑞利散射。蓝光散射得最多，大约是红光的五倍。因此，当你白天朝任何方向看天空时，都会看到蓝色的光芒。*，蓝色占主导地位，这就是为什么天空是蓝色的。如果你从月球表面看天空（你可能看过图片），你会发现天空不是蓝色的——它是黑色的，就像我们夜晚的天空一样。为什么呢？因为月球没有大气层。
Just look up in the sky and ask yourself some obvious questions: Why is the sky blue, why are sunsets red, why are clouds white? Physics has the answers! The light of the Sun is composed of all the colors of the rainbow. But as it makes its way through the atmosphere it scatters in all directions off air molecules and very tiny dust particles (much smaller than a micron, which is 1/250,000 of an inch). This is called Rayleigh scattering. Blue light scatters the most of all colors, about five times more than red light. Thus when you look at the sky during the day in any direction*, blue dominates, which is why the sky is blue. If you look at the sky from the surface of the Moon (you may have seen pictures), the sky is not blue—it’s black, like our sky at night. Why? Because the Moon has no atmosphere.
为什么日落时分天空是红色的？原因和天空是蓝色的完全相同。当太阳位于地平线附近时，它的光线需要穿过更厚的大气层，绿色、蓝色和紫色的光会被散射得最多——基本上就是被过滤掉了。当光线到达我们的眼睛——以及我们头顶的云层——时，它主要由黄色、橙色，尤其是红色组成。这就是为什么日落和日出时分天空有时看起来像是在燃烧。
Why are sunsets red? For exactly the same reason that the sky is blue. When the Sun is at the horizon, its rays have to travel through more atmosphere, and the green, blue, and violet light get scattered the most—filtered out of the light, basically. By the time the light reaches our eyes—and the clouds above us—it’s made up largely of yellow, orange, and especially red. That’s why the sky sometimes almost appears to be on fire at sunset and sunrise.
为什么云是白色的？云中的水滴比构成天空蓝色的微小颗粒大得多，当光线照射到这些大颗粒上时，所有颜色的光都会均匀散射，因此光线呈现白色。但是，如果云层非常厚，或者位于另一朵云的阴影中，那么很多光线就无法穿透云层，云层就会变成深色。
Why are clouds white? The water drops in clouds are much larger than the tiny particles that make our sky blue, and when light scatters off these much larger particles, all the colors in it scatter equally. This causes the light to stay white. But if a cloud is very thick with moisture, or if it is in the shadow of another cloud, then not much light will get through, and the cloud will turn dark.
我喜欢做的演示之一就是在教室里营造一片“蓝天”。我关掉所有的灯，然后用一束非常明亮的白色聚光灯照射教室天花板上靠近黑板的位置。聚光灯被仔细遮挡。然后我点燃几支香烟，放在光束中。烟雾颗粒非常小，足以产生瑞利散射，由于蓝光散射最强，学生们看到的是蓝色的烟雾。接下来，我进一步演示。我吸入烟雾，并在肺里停留大约一分钟——这并不总是那么容易，但科学有时需要做出牺牲。然后我松开嘴，将烟雾呼出到光束中。学生们现在看到的是白色的烟雾——我制造了一团白云！微小的烟雾颗粒在我的肺里膨胀了，因为肺里有很多水蒸气。所以现在所有颜色的光散射程度相同，散射出来的光是白色的。从蓝光到白光的颜色变化真是太神奇了！
One of the demonstrations I love to do is to create a patch of “blue sky” in my classes. I turn all the lights off and aim a very bright spotlight of white light at the ceiling of the classroom near my blackboard. The spotlight is carefully shielded. Then I light a few cigarettes and hold them in the light beam. The smoke particles are small enough to produce Rayleigh scattering, and because blue light scatters the most, the students see blue smoke. I then carry this demonstration one step further. I inhale the smoke and keep it in my lungs for a minute or so—this is not always easy, but science occasionally requires sacrifices. I then let go and exhale the smoke into the light beam. The students now see white smoke—I have created a white cloud! The tiny smoke particles have grown in my lungs, as there is a lot of water vapor there. So now all the colors scatter equally, and the scattered light is white. The color change from blue light to white light is truly amazing!
通过这个演示，我可以同时回答两个问题：为什么天空是蓝色的，为什么云是白色的？实际上，还有一个非常有趣的问题，它与光的偏振有关。我将在第五章中讨论这个问题。
With this demonstration, I’m able to answer two questions at once: Why is the sky blue, and why are clouds white? Actually, there is also a third very interesting question, having to do with the polarization of light. I’ll get to this in chapter 5.
带着学生们到郊外，我可以向他们展示仙女座星系——唯一一个肉眼可见的星系，它距离我们大约250万光年（1500万亿英里），就天文距离而言，它算是近邻了。仙女座星系由大约2000亿颗恒星组成。想象一下——2000亿颗恒星，而我们却只能把它看作是一团模糊的光斑。我们还看到了很多流星——大多数人称之为“流星”。如果你有耐心，大约每四五分钟就能看到一颗。那时候还没有人造卫星，但现在你也能看到很多。目前有两千多颗卫星绕地球运行，如果你能保持目光专注五分钟，几乎肯定能看到一颗，尤其是在日落后或日出前的几个小时内，那时太阳还没有落下或升起，阳光仍然会反射到卫星上，进入你的眼睛。卫星距离地球越远，地球日落时间和卫星所在位置日落时间的差值就越大，因此你在晚上看到它的时间就越晚。卫星之所以容易辨认，是因为它们比天空中任何其他物体（除了流星）的移动速度都快；如果它闪烁，相信我，那一定是飞机。
Out in the country with my students I could show them the Andromeda galaxy, the only one you can see with the naked eye, around 2.5 million light-years away (15 million trillion miles), which is next door as far as astronomical distances go. It’s made up of about 200 billion stars. Imagine that—200 billion stars, and we could just make it out as a faint fuzzy patch. We also spotted lots of meteorites—most people call them shooting stars. If you were patient, you’d see one about every four or five minutes. In those days there were no satellites, but now you’d see a host of those as well. There are more than two thousand now orbiting Earth, and if you can hold your gaze for five minutes you’ll almost surely see one, especially within a few hours after sunset or before sunrise, when the Sun hasn’t yet set or risen on the satellite itself and sunlight still reflects off it to your eyes. The more distant the satellite, and therefore the greater the difference in time between sunset on Earth and at the satellite, the later you can see it at night. You recognize satellites because they move faster than anything else in the sky (except meteors); if it blinks, believe me, it’s an airplane.
我一直特别喜欢向人们指出水星的存在。我们在观星。水星是距离太阳最近的行星，因此用肉眼很难观测到它。一年中只有大约二十几个清晨和傍晚是最佳观测时机。水星绕太阳公转一周只需88天，这也是它以罗马神话中速度飞快的信使之神命名的原因；而它难以观测的原因在于它的轨道离太阳非常近。从地球上看，它与太阳的夹角从未超过25度——这比手表11点钟方向时两根指针之间的夹角还要小。只有在日落后不久和日出前不久，也就是从地球上看它距离太阳最远的时候，你才能看到它。在美国，它总是接近地平线；你几乎必须身处乡村才能看到它。当你真正找到它时，那感觉真是太棒了！
I have always especially liked to point out Mercury to people when we’re stargazing. As the planet closest to the Sun, it’s very difficult to see it with the naked eye. The conditions are best only about two dozen evenings and mornings a year. Mercury orbits the Sun in just eighty-eight days, which is why it was named for the fleet-footed Roman messenger god; and the reason it’s so hard to see is that its orbit is so close to the Sun. It’s never more than about 25 degrees away from the Sun when we look at it from Earth—that’s smaller than the angle between the two hands of a watch at eleven o’clock. You can only see it shortly after sunset and before sunrise, and when it’s farthest from the Sun as seen from Earth. In the United States it’s always close to the horizon; you almost have to be in the countryside to see it. How wonderful it is when you actually find it!
观星让我们感受到宇宙的浩瀚。如果我们持续凝视夜空，让眼睛适应足够长的时间，就能清晰地看到我们银河系遥远深处的超结构——大约1000亿到2000亿颗恒星，如同编织成一幅轻盈飘逸的织物般聚集在一起，如此精妙绝伦。宇宙的浩瀚难以想象，但你可以通过观察银河系来初步了解它。
Stargazing connects us to the vastness of the universe. If we keep staring up at the night sky, and let our eyes adjust long enough, we can see the superstructure of the farther reaches of our own Milky Way galaxy quite beautifully—some 100 billion to 200 billion stars, clustered as if woven into a diaphanous fabric, so delightfully delicate. The size of the universe is incomprehensible, but you can begin to grasp it by first considering the Milky Way.
我们目前的估计是，宇宙中星系的数量可能与我们银河系中的恒星数量一样多。事实上，每当望远镜观测深空时，它看到的几乎都是星系——在极其遥远的距离上，我们根本无法分辨单个恒星——而每个星系都包含数十亿颗恒星。再比如，最近发现的已知宇宙中最大的单一结构——星系长城，它是由斯隆数字巡天项目绘制的。该项目汇集了三百多位天文学家和工程师以及二十五所大学和研究机构的共同努力。专门用于观测星系长城的斯隆望远镜每晚都在进行观测；它于2000年投入使用，并将至少持续到2014年。星系长城的长度超过十亿光年。是不是感觉晕头转向？如果没有，那么请想想，可观测宇宙（并非整个宇宙，只是我们能够观测到的部分）的直径约为900亿光年。
Our current estimate is that there may be as many galaxies in the universe as there are stars in our own galaxy. In fact, whenever a telescope observes deep space, what it sees is mostly galaxies—it’s impossible to distinguish single stars at truly great distances—and each contains billions of stars. Or consider the recent discovery of the single largest structure in the known universe, the Great Wall of galaxies, mapped by the Sloan Digital Sky Survey, a major project that has combined the efforts of more than three hundred astronomers and engineers and twenty-five universities and research institutions. The dedicated Sloan telescope is observing every night; it went into operation in the year 2000 and will continue till at least the year 2014. The Great Wall is more than a billion light-years long. Is your head spinning? If not, then consider that the observable universe (not the entire universe, just the part we can observe) is roughly 90 billion light-years across.
这就是物理学的力量；它可以告诉我们，我们可观测的宇宙宇宙由大约1000亿个星系组成。它还能告诉我们，在我们可见的宇宙中，只有大约4%是普通物质，构成恒星、星系（以及你我）的物质就是由这些普通物质构成的。大约23%是所谓的暗物质（它是不可见的）。我们知道它的存在，但我们不知道它是什么。剩下的73%，也就是宇宙中大部分的能量，被称为暗能量，它也是不可见的。没有人知道它是什么。总而言之，我们对宇宙中96%的质量/能量一无所知。物理学已经解释了很多，但我们仍然有很多谜团需要解开，这让我感到非常振奋。
This is the power of physics; it can tell us that our observable universe is made up of some 100 billion galaxies. It can also tell us that of all the matter in our visible universe, only about 4 percent is ordinary matter, of which stars and galaxies (and you and I) are made. About 23 percent is what’s called dark matter (it’s invisible). We know it exists, but we don’t know what it is. The remaining 73 percent, which is the bulk of the energy in our universe, is called dark energy, which is also invisible. No one has a clue what that is either. The bottom line is that we’re ignorant about 96 percent of the mass/energy in our universe. Physics has explained so much, but we still have many mysteries to solve, which I find very inspiring.
物理学探索着难以想象的浩瀚宇宙，但同时它也能深入到极其微小的领域，例如中微子这类物质的微小粒子，小到只有质子的一小部分。我早期从事物理学研究时，大部分时间都花在了微观世界，测量和绘制放射性原子核释放粒子和辐射的轨迹。这属于核物理，但并非制造原子弹的那种。我研究的是物质在最基本的层面上是如何运作的。
Physics explores unimaginable immensity, but at the same time it can dig down into the very smallest realms, to the very bits of matter such as neutrinos, as small as a tiny fraction of a proton. That is where I was spending most of my time in my early days in the field, in the realms of the very small, measuring and mapping the release of particles and radiation from radioactive nuclei. This was nuclear physics, but not the bomb-making variety. I was studying what made matter tick at a really basic level.
你可能知道，几乎所有你能看见和触摸到的物质都是由元素构成的，例如氢、氧和碳，它们结合成分子。元素的最小单位是原子，原子由原子核和电子组成。原子核由质子和中子组成。宇宙中最轻、含量最丰富的元素氢，只有一个质子和一个电子。但是，氢还有一种同位素，它的原子核中除了质子外还有一个中子。这种同位素是氢的同位素，是同一种元素的不同形式，叫做氘。甚至还有第三种氢同位素，它的原子核中除了质子外还有两个中子，叫做氚。同一种元素的所有同位素都具有相同数量的质子，但中子数量不同，而且不同的元素拥有不同数量的同位素。例如，氧有十三种同位素，金有三十六种同位素。
You probably know that almost all the matter you can see and touch is made up of elements, such as hydrogen, oxygen, and carbon combined into molecules, and that the smallest unit of an element is an atom, made up of a nucleus and electrons. A nucleus, recall, consists of protons and neutrons. The lightest and most plentiful element in the universe, hydrogen, has one proton and one electron. But there is a form of hydrogen that has a neutron as well as a proton in its nucleus. That is an isotope of hydrogen, a different form of the same element; it’s called deuterium. There’s even a third isotope of hydrogen, with two neutrons joining the proton in the nucleus; that’s called tritium. All isotopes of a given element have the same number of protons, but a different number of neutrons, and elements have different numbers of isotopes. There are thirteen isotopes of oxygen, for instance, and thirty-six isotopes of gold.
现在，这些同位素中有很多是稳定的——也就是说，它们几乎可以永远存在。但大多数是不稳定的，换句话说，它们……放射性物质及其同位素都会衰变：也就是说，它们迟早会转化为其他元素。有些转化后的元素是稳定的，衰变随即停止；而另一些则不稳定，衰变会持续进行，直到达到稳定状态。氢的三种同位素中，只有氚是放射性的——它会衰变成稳定的氦同位素。氧的十三种同位素中，有三种是稳定的；金的三十六种同位素中，只有一种是稳定的。
Now, many of these isotopes are stable—that is, they can last more or less forever. But most are unstable, which is another way of saying they’re radioactive, and radioactive isotopes decay: that is to say, sooner or later they transform themselves into other elements. Some of the elements they transform into are stable, and then the radioactive decay stops, but others are unstable, and then the decay continues until a stable state is reached. Of the three isotopes of hydrogen, only one, tritium, is radioactive—it decays into a stable isotope of helium. Of the thirteen isotopes of oxygen, three are stable; of gold’s thirty-six isotopes, only one is stable.
你可能还记得，我们用“半衰期”来衡量放射性同位素的衰变速度——半衰期可以从微秒（百万分之一秒）到数十亿年不等。如果我们说氚的半衰期约为十二年，这意味着在给定的氚样本中，一半的同位素会在十二年内衰变（二十四年后只剩下四分之一）。核衰变是许多不同元素转化和生成的最重要过程之一。这并非炼金术。事实上，在我攻读博士学位期间，我经常观察到放射性金同位素衰变成汞，而不是像中世纪炼金术士所希望的那样反过来。然而，汞和铂都有许多同位素会衰变成金。但只有一种铂同位素和一种汞同位素会衰变成稳定的金，也就是你可以戴在手指上的那种金。
You will probably remember that we measure how quickly radioactive isotopes decay by their “half-life”—which can range from a microsecond (one-millionth of a second) to billions of years. If we say that tritium has a half-life of about twelve years, we mean that in a given sample of tritium, half of the isotopes will decay in twelve years (only one-quarter will remain after twenty-four years). Nuclear decay is one of the most important processes by which many different elements are transformed and created. It’s not alchemy. In fact, during my PhD research, I was often watching radioactive gold isotopes decay into mercury rather than the other way around, as the medieval alchemists would have liked. There are, however, many isotopes of mercury, and also of platinum, that decay into gold. But only one platinum isotope and only one mercury isotope decay into stable gold, the kind you can wear on your finger.
这项工作令人无比兴奋；我亲手就能感受到放射性同位素的衰变过程。而且工作强度非常大。我研究的同位素半衰期通常只有一天或几天。例如，金-198的半衰期只有两天半多一点，所以我必须争分夺秒。我会从代尔夫特开车到阿姆斯特丹，那里用回旋加速器制造这些同位素，然后再赶回代尔夫特的实验室。在那里，我会把同位素溶解在酸中，使它们变成液体，然后滴在极薄的薄膜上，最后放入探测器中。
The work was immensely exciting; I would have radioactive isotopes literally decaying in my hands. And it was very intense. The isotopes I was working with typically had half-lives of only a day or a few days. Gold-198, for instance, has a half-life of a little over two and a half days, so I had to work fast. I would drive from Delft to Amsterdam, where they used a cyclotron to make these isotopes, and rush back to the lab at Delft. There I would dissolve the isotopes in an acid to get them into liquid form, put them on very thin film, and place them into detectors.
我当时试图验证一个关于核衰变的理论，该理论预测了原子核发射伽马射线与电子的比例，而我的工作需要精确的测量。这项工作已经针对许多放射性同位素完成，但最近的一些测量结果与该理论的预测有所不同。我的导师，阿尔德特·瓦普斯特拉教授建议我尝试确定问题究竟出在理论还是测量上。这让我很有成就感，就像在解一个极其复杂的谜题。难点在于，我的测量结果必须比之前其他研究人员的测量结果精确得多。
I was trying to verify a theory about nuclear decay, one that predicted the ratio of gamma ray to electron emissions from the nuclei, and my work required precise measurements. This work had already been done for many radioactive isotopes, but some recent measurements had come out that were different from what the theory predicted. My supervisor, Professor Aaldert Wapstra, suggested I try to determine whether it was the theory or the measurements that were at fault. It was enormously satisfying, like working on a fantastically intricate puzzle. The challenge was that my measurements had to be much more precise than the ones those other researchers had come up with before me.
电子极其微小，以至于有人说它们没有有效尺寸——它们的直径不到一千万亿分之一厘米——而伽马射线的波长不到十亿分之一厘米。然而，物理学却为我提供了探测和计数它们的方法。这正是我热爱实验物理学的另一个原因：它让我们能够“触及”不可见的事物。
Electrons are so small that some say they have no effective size—they’re less than a thousand-trillionth of a centimeter across—and gamma rays have a wavelength of less than a billionth of a centimeter. And yet physics had provided me with the means to detect and to count them. That’s yet another thing that I love about experimental physics; it lets us “touch” the invisible.
为了获得所需的测量数据，我必须尽可能长时间地提取样本，因为计数越多，精度就越高。我经常连续工作60个小时，常常不睡觉。我变得有点着迷了。
To get the measurements I needed, I had to milk the sample as long as I could, because the more counts I had, the greater my precision would be. I’d frequently be working for something like 60 hours straight, often without sleeping. I became a little obsessed.
对于实验物理学家来说，精确性至关重要。准确度是唯一重要的指标，任何测量结果如果不能同时标明其准确度，都毫无意义。这个简单、有力且极其基础的理念，在大学物理教材中几乎总是被忽略。了解准确度对我们生活中的许多方面都至关重要。
For an experimental physicist, precision is key in everything. The accuracy is the only thing that matters, and a measurement that doesn’t also indicate its degree of accuracy is meaningless. This simple, powerful, totally fundamental idea is almost always ignored in college books about physics. Knowing degrees of accuracy is critical to so many things in our lives.
在我从事放射性同位素研究的过程中，要达到所需的精度非常具有挑战性，但在三四年的时间里，我的测量技术不断进步。改进了一些探测器之后，它们的精度达到了极高的水平。我验证了理论，并发表了我的研究成果，这项工作最终成为了我的博士论文。令我特别欣慰的是，我的结果相当确凿，这种情况并不常见。在物理学乃至整个科学领域，很多时候结果并非总是清晰明了。我很幸运能够得出确切的结论。我解开了一个谜题，确立了自己作为物理学家的地位，并且帮助探索了亚原子世界的未知领域。当时我29岁，能够做出如此重要的贡献，我感到无比激动。并非每个人都能如此幸运。像牛顿和爱因斯坦那样做出巨大的基础性发现固然重要，但仍有很多领域有待探索。
In my work with radioactive isotopes, attaining the degree of accuracy I had to achieve was very challenging, but over three or four years I got better and better at the measurements. After I improved some of the detectors, they turned out to be extremely accurate. I was confirming the theory, and publishing my results, and this work ended up being my PhD thesis. What was especially satisfying to me was that my results were rather conclusive, which doesn’t happen very often. Many times in physics, and in science generally, results are not always clear-cut. I was fortunate to arrive at a firm conclusion. I had solved a puzzle and established myself as a physicist, and I had helped to chart the unknown territory of the subatomic world. I was twenty-nine years old, and I was thrilled to be making a solid contribution. Not all of us are destined to make gigantic fundamental discoveries like Newton and Einstein did, but there’s an awful lot of territory that is still ripe for exploration.
我很幸运，在我获得学位的时候，一个关于宇宙本质的全新发现时代正拉开帷幕。天文学家们正以惊人的速度取得各种发现。一些人正在研究火星和金星的大气层，寻找水蒸气。一些人发现了环绕地球磁力线的带电粒子带，我们现在称之为范艾伦辐射带。另一些人则发现了被称为类星体（准恒星射电源）的巨大而强大的射电波源。宇宙微波背景辐射（CMB）于1965年被发现——这是宇宙大爆炸释放能量的痕迹，为曾经备受争议的宇宙大爆炸起源理论提供了强有力的证据。不久之后，在1967年，天文学家发现了一种新的恒星类型，后来被称为脉冲星。
I was also fortunate that at the time I got my degree, a whole new era of discovery about the nature of the universe was getting under way. Astronomers were making discoveries at an amazing pace. Some were examining the atmospheres of Mars and Venus, searching for water vapor. Some had discovered the belts of charged particles circling the Earth’s magnetic field lines, which we now call the Van Allen belts. Others had discovered huge, powerful sources of radio waves known as quasars (quasi-stellar radio sources). The cosmic microwave background (CMB) radiation was discovered in 1965—the traces of the energy released by the big bang, powerful evidence for the big bang theory of the universe’s origin, which had been controversial. Shortly after, in 1967, astronomers would discover a new category of stars, which came to be called pulsars.
我或许会继续从事核物理方面的工作，因为那个领域也涌现出了许多新的发现。这项工作主要集中在寻找和发现数量迅速增长的亚原子粒子群，其中最重要的是被称为夸克的粒子，它们后来被证实是质子和中子的组成单元。夸克的行为非常奇特，为了对其进行分类，物理学家给它们赋予了“味”的概念：上夸克、下夸克、奇异夸克、粲夸克、顶夸克和底夸克。夸克的发现是科学史上一个激动人心的时刻，它证实了一个纯粹的理论构想。理论学家预测了夸克的存在，而实验学家则成功地发现了它们。它们是多么奇特啊，揭示了物质的构成远比我们之前所知的要复杂得多。例如，我们现在知道质子由两个上夸克和一个下夸克组成，它们通过强核力结合在一起，而这种强核力又以被称为胶子的奇异粒子的形式存在。最近一些理论学家计算得出，上夸克的质量约为质子的0.2%，而下夸克的质量约为质子的0.5%。这已经不是你祖父辈记忆中的原子核了。粒子动物园肯定是一个引人入胜的研究领域，但幸运的是，我之前掌握的测量原子核辐射的技能，最终却在探索宇宙方面发挥了极其重要的作用。1965年，我收到了麻省理工学院布鲁诺·罗西教授的邀请，从事X射线天文学的研究。当时，X射线天文学还是一个全新的领域，实际上只有几年的历史——罗西教授于1959年开创了这一领域。
I might have continued working in nuclear physics, as there was a great deal of discovery going on there as well. This work was mostly in the hunt for and discovery of a rapidly growing zoo of subatomic particles, most importantly those called quarks, which turned out to be the building blocks of protons and neutrons. Quarks are so odd in their range of behaviors that in order to classify them, physicists assigned them what they called flavors: up, down, strange, charm, top, and bottom. The discovery of quarks was one of those beautiful moments in science when a purely theoretical idea is confirmed. Theorists had predicted quarks, and then experimentalists managed to find them. And how exotic they were, revealing that matter was so much more complicated in its foundations than we had known. For instance, we now know that protons consist of two up quarks and one down quark, held together by the strong nuclear force, in the form of other strange particles called gluons. Some theoreticians have recently calculated that the up quark seems to have a mass of about 0.2 percent of that of a proton, while the down quark has a mass of about 0.5 percent of the mass of a proton. This was not your grandfather’s nucleus anymore. The particle zoo would have been a fascinating area of research to go into, I’m sure, but by a happy accident, the skills I’d learned for measuring radiation emitted from the nucleus turned out to be extremely useful for probing the universe. In 1965, I received an invitation from Professor Bruno Rossi at MIT to work on X-ray astronomy, which was an entirely new field, really just a few years old at the time—Rossi had initiated it in 1959.
麻省理工学院是我人生中最美好的事情。罗西在宇宙射线领域的研究早已闻名遐迩。二战期间，他曾领导洛斯阿拉莫斯国家实验室的一个部门，并在太阳风（也称行星际等离子体）的测量方面做出了开创性贡献。太阳风是由太阳喷射出的带电粒子流，它不仅造成了北极光，还将彗星的尾巴吹离太阳。如今，他萌生了在宇宙中寻找X射线的想法。这完全是一项探索性的工作；他当时并不知道能否找到X射线。
MIT was the best thing that could ever have happened to me. Rossi’s work on cosmic rays was already legendary. He’d headed a department at Los Alamos during the war and pioneered in the measurements of solar wind, also called interplanetary plasma—a stream of charged particles ejected by the Sun that causes our aurora borealis and “blows” comet tails away from the Sun. Now he had the idea to search the cosmos for X-rays. It was completely exploratory work; he had no idea whether he’d find them or not.
当时在麻省理工学院，一切皆有可能。只要你能说服别人相信某个想法可行，你就可以着手去做。这和荷兰简直天壤之别！在代尔夫特理工大学，等级森严，研究生被视为低人一等。教授们有我所在教学楼正门的钥匙，而研究生却只能拿到地下室的钥匙，那里存放着自行车。每次进楼，你都得小心翼翼地穿过自行车存放室，时刻提醒自己，你不过是个微不足道的存在。
Anything went at that time at MIT. Any idea you had, if you could convince people that it was doable, you could work on it. What a difference from the Netherlands! At Delft, there was a rigid hierarchy, and the graduate students were treated like a lower class. The professors were given keys to the front door of my building, but as a graduate student you only got a key to the door in the basement, where the bicycles were kept. Each time you entered the building you had to pick your way through the bicycle storage rooms and be reminded of the fact that you were nothing.
如果你想在五点以后工作，就必须每天下午四点前填写一份表格，说明你为什么需要加班，而我几乎每次都得这么做。这种官僚作风真是令人厌烦。
If you wanted to work after five o’clock you had to fill out a form, every day, by four p.m., justifying why you had to stay late, which I had to do almost all the time. The bureaucracy was a real nuisance.
我所在研究所的三位教授都预留了靠近正门的停车位。其中一位，也是我的导师，在阿姆斯特丹工作，每周二才来代尔夫特一次。有一天我问他：“您不在的时候，我可以借用一下您的停车位吗？” 他说：“当然可以。” 但就在我把车停在那里的第一天，我就被广播叫到，并被告知……他们用最严厉的措辞要求我把车开走。还有一件事。因为我得去阿姆斯特丹取我的同位素，所以他们允许我花25美分买一杯咖啡，1.25荷兰盾吃午饭（当时1.25荷兰盾大约是1美元的三分之一），但我必须分别提交收据。于是我问能不能把那25美分加到午饭的收据里，只提交一张1.50荷兰盾的收据。系主任布莱斯教授给我写了一封信，信里说如果我想吃大餐，可以自费。
The three professors in charge of my institute had reserved parking places close to the front door. One of them, my own supervisor, worked in Amsterdam and came to Delft only once a week on Tuesdays. I asked him one day, “When you are not here, would you mind if I used your parking space?” He said, “Of course not,” but then the very first day I parked there I was called on the public intercom and instructed in the strongest terms possible that I was to remove my car. Here’s another one. Since I had to go to Amsterdam to pick up my isotopes, I was allowed 25 cents for a cup of coffee, and 1.25 guilders for lunch (1.25 guilders was about one-third of a U.S. dollar at the time), but I had to submit separate receipts for each. So I asked if I could add the 25 cents to the lunch receipt and only submit one receipt for 1.50 guilders. The department chair, Professor Blaisse, wrote me a letter that stated that if I wanted to have gourmet meals I could do so—at my own expense.
所以，能来到麻省理工学院，摆脱这一切，真是太棒了；我感觉自己获得了新生。这里的一切都是为了鼓励我。我拿到了一把大门的钥匙，可以随心所欲地在办公室里工作，白天黑夜都行。对我来说，那把大楼的钥匙就像是打开一切的钥匙。1966年6月，也就是我到校六个月后，物理系主任就给了我一个教职。我接受了，而且一直留在这里。
So what a joy it was to get to MIT and be free from all of that; I felt reborn. Everything was done to encourage you. I got a key to the front door and could work in my office day or night just as I wanted. To me, that key to the building was like a key to everything. The head of the Physics Department offered me a faculty position six months after my arrival, in June of 1966. I accepted and I’ve never left.
来到麻省理工学院也让我无比兴奋，因为我曾亲身经历过二战的浩劫。纳粹杀害了我一半的家人，这场悲剧我至今仍难以释怀。我偶尔会谈起这件事，但很少，因为它对我来说太过痛苦——虽然已经过去六十五年多了，但那段经历依然让我难以承受。我和妹妹比阿特丽斯谈起这件事时，几乎都会忍不住落泪。
Arriving at MIT was also so exhilarating because I had lived through the devastation of World War II. The Nazis had murdered half of my family, a tragedy that I haven’t really digested yet. I do talk about it sometimes, but very rarely because it’s so very difficult for me—it is more than sixty-five years ago, and it’s still overwhelming. When my sister Bea and I talk about it, we almost always cry.
我出生于1936年，1940年5月10日德国入侵荷兰时，我才四岁。我最早的记忆之一，就是我们全家——外公外婆、我的父母、妹妹和我——躲在位于海牙阿曼德尔街61号的家里的浴室里，当时纳粹军队正进入我的国家。我们用湿手帕捂住鼻子，因为之前已经收到过毒气袭击的警告。
I was born in 1936, and I was just four years old when the Germans attacked the Netherlands on May 10, 1940. One of my earliest memories is all of us, my mother’s parents, my mother and father and sister and I, hiding in the bathroom of our house (at the Amandelstraat 61 in The Hague) as the Nazi troops entered my country. We were holding wet handkerchiefs over our noses, as there had been warnings that there would be gas attacks.
1942年，荷兰警察从我的犹太祖父母古斯塔夫·莱文·戈特菲尔德和艾玛·莱文·戈特菲尔德家中将他们抓走。几乎在同一时间，他们又抓走了我父亲的妹妹朱莉娅、她的丈夫雅各布（绰号“詹诺”）以及他们的三个孩子——奥托、鲁迪和艾米——并将他们连同行李一起塞进卡车，送往荷兰的韦斯特博克集中营。超过十万犹太人被送往那里。他们途经韦斯特博克集中营，前往其他集中营。纳粹迅速将我的祖父母送往奥斯维辛集中营，并在他们抵达当天——1942年11月19日——就将他们杀害——用毒气杀害。我的祖父当时75岁，祖母69岁，所以他们不符合被送往劳改营的条件。相比之下，韦斯特博克集中营却非常奇特；它被布置成犹太人的度假胜地。那里有芭蕾舞表演和商店。我的母亲经常烤土豆煎饼，然后邮寄给我们在韦斯特博克的家人。
The Dutch police snatched my Jewish grandparents, Gustav Lewin and Emma Lewin Gottfeld, from their house in 1942. At about the same time they hauled out my father’s sister Julia, her husband Jacob (called Jenno), and her three children—Otto, Rudi, and Emmie—and put them all on trucks, with their suitcases, and sent them to Westerbork, the transshipment camp in Holland. More than a hundred thousand Jews passed through Westerbork, on their way to other camps. The Nazis quickly sent my grandparents to Auschwitz and murdered them—gassed them—the day they arrived, November 19, 1942. My grandfather was seventy-five and my grandmother sixty-nine, so they wouldn’t have been candidates for labor camps. Westerbork, by contrast, was so strange; it was made to look like a resort for Jews. There were ballet performances and shops. My mother would often bake potato pancakes that she would then send by mail to our family in Westerbork.
因为我的叔叔詹诺是荷兰人所说的“无国籍人士”（ statenloos），他没有国籍，所以他才能拖延时间，和家人一起在韦斯特博克集中营待了十五个月，直到纳粹将他们一家人分开，送往不同的集中营。他们先把我的姑姑朱莉娅和我的表兄妹艾米和鲁迪送到德国的拉文斯布吕克女子集中营，然后又送到同样位于德国的贝尔根-贝尔森集中营，在那里他们一直被囚禁到战争结束。我的姑姑朱莉娅在盟军解放集中营十天后去世，但我的表兄妹们幸存了下来。我的表兄奥托是年纪最大的，他也曾被送往拉文斯布吕克，被关押在那里的男子集中营，在战争接近尾声时，他最终被送往萨克森豪森集中营；他在 1945 年 4 月的萨克森豪森死亡行军中幸存了下来。他的叔叔詹诺被直接送往布痕瓦尔德集中营，在那里他和 55000 多人一起被杀害。
Because my uncle Jenno was what the Dutch call “statenloos,” or stateless—he had no nationality—he was able to drag his feet and stay at Westerbork with his family for fifteen months before the Nazis split up the family and shipped them to different camps. They sent my aunt Julia and my cousins Emmie and Rudi first to the women’s concentration camp Ravensbrück in Germany and then to Bergen-Belsen, also in Germany, where they were imprisoned until the war ended. My aunt Julia died ten days after the camp’s liberation by the Allies, but my cousins survived. My cousin Otto, the oldest, had also been sent to Ravensbrück, to the men’s camp there, and near the end of the war ended up in the concentration camp in Sachsenhausen; he survived the Sachsenhausen death march in April 1945. Uncle Jenno they sent directly to Buchenwald, where they murdered him—along with more than 55,000 others.
每当我看一部关于大屠杀的电影（很长一段时间我都不敢看），我都会立刻把电影里的情节投射到自己的家人身上。这就是为什么我觉得《美丽人生》这部电影非常难看，甚至令人反感。我实在无法想象有人会拿如此严肃的事情开玩笑。我至今仍然会反复做噩梦，梦见自己被纳粹追赶，有时还会从噩梦中惊醒，恐惧万分。我甚至有一次在梦里亲眼目睹了自己被纳粹处决。
Whenever I see a movie about the Holocaust, which I would not do for a really long time, I project it immediately onto my own family. That’s why I felt the movie Life Is Beautiful was terribly difficult to watch, even objectionable. I just couldn’t imagine joking about something that was so serious. I still have recurring nightmares about being chased by Nazis, and I wake up sometimes absolutely terrified. I even once in my dreams witnessed my own execution by the Nazis.
总有一天，我想走一遍我祖父母生前最后走过的路——从火车站到奥斯维辛集中营的毒气室。我不知道自己是否真的能做到，但我觉得这是纪念他们的一种方式。面对如此惨绝人寰的暴行，或许我们所能做的只有这些微小的举动。还有，我们拒绝遗忘：我从不谈论我的家人。他们“死于”集中营。我总是用“被谋杀”这个词，这样我们才不会让语言掩盖真相。
Some day I would like to take the walk, my paternal grandparents’ last walk, from the train station to the gas chambers at Auschwitz. I don’t know if I’ll ever do it, but it seems to me like one way to memorialize them. Against such a monstrosity, maybe small gestures are all that we have. That, and our refusal to forget: I never talk about my family members having “died” in concentration camps. I always use the word murdered, so we do not let language hide the reality.
我父亲是犹太人，母亲不是。作为一名娶了非犹太妻子的犹太人，他起初并没有成为纳粹的目标。但到了1943年，他很快就成了目标。我记得他必须佩戴黄色的犹太星。我的母亲、妹妹和我都没有佩戴，但他必须佩戴。我们一开始并没有太在意。他把犹太星藏在衣服下面，这是被禁止的。真正令人恐惧的是，他逐渐适应了纳粹的种种限制，而这些限制却越来越严苛。起初，他不被允许乘坐公共交通工具。后来，他不被允许进入公园。再后来，他不被允许进入餐馆；在他曾经经常光顾的地方，他成了不受欢迎的人！而最不可思议的是人们的适应能力。
My father was Jewish but my mother was not, and as a Jew married to a non-Jewish woman, he was not immediately a target. But he became a target soon enough, in 1943. I remember that he had to wear the yellow star. Not my mother, or sister, or I, but he did. We didn’t pay much attention to it, at least not at first. He had it hidden a little bit, under his clothes, which was forbidden. What was really frightening was the way he gradually accommodated to the Nazi restrictions, which just kept getting worse. First, he was not allowed on public transportation. Then, he wasn’t allowed in public parks. Then he wasn’t allowed in restaurants; he became persona non grata in places he had frequented for years! And the incredible thing is the ability of people to adjust.
当他不能再乘坐公共交通工具时，他会说：“那我多久坐一次公共交通工具呢？”当他不能再去公园时，他会说：“那我多久去一次公园呢？”后来，当他不能去餐馆时，他又会说：“那我多久去一次餐馆呢？”他试图把这些糟糕的事情说得无关紧要，就像一些小小的麻烦，也许是为了孩子，也许也是为了让自己心安。我不知道。
When he could no longer take public transportation, he would say, “Well, how often do I make use of public transportation?” When he wasn’t allowed in public parks anymore, he would say, “Well, how often do I go to public parks?” Then, when he could not go to a restaurant, he would say, “Well, how often do I go to restaurants?” He tried to make these awful things seem trivial, like a minor inconvenience, perhaps for his children’s sake, and perhaps also for his own peace of mind. I don’t know.
这仍然是我最难启齿的事情之一。为什么他们明明看到水位慢慢上涨，却意识不到自己会被淹死？他们怎么能同时看到又看不到呢？我无法理解。当然，从某种意义上说，这完全可以理解；或许这是唯一的生存之道，只要他们还能自欺欺人。
It’s still one of the hardest things for me to talk about. Why this ability to slowly see the water rise but not recognize that it will drown you? How could they see it and not see it at the same time? That’s something that I cannot cope with. Of course, in a sense it’s completely understandable; perhaps that’s the only way you can survive, for as long as you are able to fool yourself.
尽管纳粹禁止犹太人进入公共公园，但我父亲却被允许在墓地散步。直到现在，我仍然记得和他一起在附近墓地散步的时光。我们会一起想象家人去世的原因和方式——有时一天之内会有四个人去世。如今，每当我漫步在剑桥著名的奥本山公墓时，我仍然会这样做。
Though the Nazis made public parks off-limits to Jews, my father was allowed to walk in cemeteries. Even now, I recall many walks with him at a nearby cemetery. We fantasized about how and why family members died—sometimes four had died on the same day. I still do that nowadays when I walk in Cambridge’s famous Mount Auburn Cemetery.
我成长过程中发生的最戏剧性的事情是……父亲突然消失了。我清楚地记得他离开的那天。那天我放学回家，隐隐觉得他不见了。母亲不在家，我就问保姆莱妮：“爸爸去哪儿了？”她给了我一些安慰的回答，但我心里清楚，父亲已经离开了。
The most dramatic thing that happened to me growing up was that all of a sudden my father disappeared. I vividly remember the day he left. I came home from school and sensed somehow that he was gone. My mother was not home, so I asked our nanny, Lenie, “Where’s Dad?” and I got an answer of some sort, meant to be reassuring, but somehow I knew that my father had left.
贝娅看到他离开，但她直到很多年后才告诉我。为了安全起见，我们四个人睡在同一间卧室。凌晨四点，她看到他起床，把一些衣服装进包里。然后他吻了我母亲，就离开了。我母亲不知道他要去哪里；如果知道的话，对她来说非常危险，因为德国人可能会拷问她，逼问出我父亲的下落，而她肯定会告诉他们。我们现在知道是抵抗组织藏匿了他，最终我们也通过抵抗组织收到了他的一些消息，但当时不知道他在哪里，甚至不知道他是否还活着，真是太可怕了。
Bea saw him leaving, but she never told me until many years later. The four of us slept in the same bedroom for security, and at four in the morning, she saw him get up and put some clothes in a bag. Then he kissed my mother and left. My mother didn’t know where he was going; that knowledge would have been very dangerous, because the Germans might have tortured her to find out where my father was and she would have told them. We now know that the Resistance hid him, and eventually we got some messages from him through the Resistance, but at the time it was absolutely terrible not knowing where he was or even if he was alive.
我当时年纪太小，还不明白他的离世对母亲的影响有多么深远。我的父母在家办了一所学校——这无疑对我热爱教学产生了深远的影响——没有他，母亲的生活举步维艰。她原本就有些抑郁的倾向，如今丈夫去世，她担心我们这些孩子会被送进集中营。她一定非常害怕，因为——正如她五十五年后告诉我的那样——一天晚上，她让我和比阿特丽斯睡在厨房里，然后她把窗帘、毯子和毛巾塞到门缝下，不让空气流通。她原本打算打开煤气，让我们睡到死，但她最终没有这么做。谁又能责怪她有这样的想法呢？——我知道我和比阿特丽斯都不会。
I was too young to understand how profoundly his absence affected my mother. My parents ran a school out of our home—which no doubt had a strong influence on my love of teaching—and she struggled to carry on without him. She had a tendency toward depression anyway, but now her husband was gone, and she worried that we children might be sent to a concentration camp. She must have been truly terrified for us because—as she told me fifty-five years later—one night she said to Bea and me that we should sleep in the kitchen, and she stuffed curtains and blankets and towels under the doors so that no air could escape. She was intending to put the gas on and let us sleep ourselves into death, but she didn’t go through with it. Who can blame her for thinking of it—I know that Bea and I don’t.
我当时很害怕。我知道这听起来很荒谬，但我是家里唯一的男孩，所以即使只有七八岁，我也算是家里的顶梁柱。我们住在海牙，那里沿海有很多破败的房子，都被德国人毁了一半，他们在我们的海滩上修建碉堡。我会去那些房子里偷木头——我本来想说“收集”，但那确实是偷——这样我们才有柴火做饭和取暖。
I was afraid a lot. And I know it sounds ridiculous, but I was the only male, so I sort of became the man of the house, even at age seven and eight. In The Hague, where we lived, there were many broken-down houses on the coast, half-destroyed by the Germans who were building bunkers on our beaches. I would go there and steal wood—I was going to say “collect,” but it was stealing—from those houses so that we had some fuel for cooking and for heat.
为了在冬天保暖，我们穿那种粗糙、扎人、质量低劣的羊毛衫。直到今天，我仍然无法忍受羊毛。我的皮肤非常敏感，所以睡在八百支纱的纯棉床单上。这也是为什么我订购的都是非常精细的纯棉衬衫——不会刺激我皮肤的那种。我的女儿宝琳告诉我，如果我看到她穿羊毛衫，我仍然会不自觉地避开；战争对我的影响至今犹存。
To try to stay warm in the winters we wore this rough, scratchy, poor-quality wool. And I still cannot stand wool to this day. My skin is so sensitive that I sleep on eight-hundred-thread-count cotton sheets. That’s also why I order very fine cotton shirts—ones that do not irritate my skin. My daughter Pauline tells me that if I see her wearing wool, I still turn away; such is the effect the war still has on me.
我父亲在战争仍在进行时，于1944年秋天返回。家里人对这件事的来龙去脉说法不一，但据我所知，大概是这样的：我亲爱的姑姑劳克（我母亲的妹妹）有一天在阿姆斯特丹——离海牙大约30英里——看到了我父亲！她远远地跟着他，看到他走进了一栋房子。后来她又去了阿姆斯特丹，发现他和一个女人住在一起。
My father returned while the war was still going on, in the fall of 1944. People in my family disagree about just how this happened, but as near as I can tell it seems that my wonderful aunt Lauk, my mother’s sister, was in Amsterdam one day, about 30 miles away from The Hague, and she caught sight of my father! She followed him from a distance and saw him go into a house. Later she went back and discovered that he was living with a woman.
我姑姑把这件事告诉了我母亲，母亲起初更加沮丧难过，但据说她很快振作起来，乘船去了阿姆斯特丹（当时火车已经停运了），径直走到房子前，按响了门铃。那女人走了出来，我母亲说：“我要见我的丈夫。”女人回答说：“我是莱文先生的妻子。”但我母亲坚持说：“我要见我的丈夫。”我父亲来到门口，那女人说：“我给你五分钟时间收拾东西跟我回去，否则你可以离婚，以后再也见不到你的孩子。”三分钟后，我父亲带着东西下楼，跟她一起回来了。
My aunt told my mother, who at first got even more depressed and upset, but I’m told that she collected herself and took the boat to Amsterdam (trains were no longer operating), marched right up to the house, and rang the bell. Out came the woman, and my mother said, “I want to speak to my husband.” The woman replied, “I am the wife of Mr. Lewin.” But my mother insisted: “I want my husband.” My father came to the door, and she said, “I’ll give you five minutes to pack up and come back with me or else you can get a divorce and you’ll never see your children again.” In three minutes he came back downstairs with his things and returned with her.
在某些方面，他回来后情况更糟，因为人们都知道我父亲（也叫沃尔特·莱文）是犹太人。抵抗组织给了他假身份证，名字是雅普·霍斯特曼，我和妹妹被指示叫他雅普叔叔。这简直是个奇迹，直到今天我和比阿都想不明白，但竟然没有人告发他。一个木匠在我们家一楼开了个小门。我们可以把小门掀开，父亲就可以下去躲在里面的狭小空间里。不可思议的是，父亲竟然成功躲过了抓捕。
In some ways it was much worse when he was back, because people knew that my father, whose name was also Walter Lewin, was a Jew. The Resistance had given him false identification papers, under the name of Jaap Horstman, and my sister and I were instructed to call him Uncle Jaap. It’s a total miracle, and doesn’t make any sense to Bea and me to this very day, but no one turned him in. A carpenter made a hatch in the ground floor of our house. We could lift it up and my father could go down and hide in the crawl space. Remarkably, my father managed to avoid capture.
战争结束前大约八个月，他可能一直在家。其中包括战争期间我们最艰难的时期——1944年的饥荒，也就是所谓的“饥荒之冬”。人们饿死了——将近两万人丧生。为了取暖，我们爬到房子底下，把每隔一根楼板横梁——支撑底层的大梁——都拆下来当柴烧。在那个饥荒之冬，我们吃郁金香球茎，甚至树皮。人们可以把我父亲交给德国人换取食物。德国人还会给每个被交出的犹太人一笔钱（我记得是五十荷兰盾，当时大约相当于十五美元）。
He was probably at home eight months or so before the war ended, including the worst time of the war for us, the winter of 1944 famine, the hongerwinter. People starved to death—nearly twenty thousand died. For heat we crawled under the house and pulled out every other floor joist—the large beams that supported the ground floor—for firewood. In the hunger winter we ate tulip bulbs, and even bark. People could have turned my father in for food. The Germans would also pay money (I believe it was fifty guilders, which was about fifteen dollars at the time) for every Jew they turned in.
有一天，德国人真的来过我们家。原来他们是来收集打字机的，他们看了看我们家的，就是以前教打字用的那种，但他们觉得太旧了。德国人真是蠢到家了；既然他们被要求收集打字机，又怎么会去收集犹太人呢？我知道，这听起来像电影情节。但这事儿真的发生过。
The Germans did come to our house one day. It turned out that they were collecting typewriters, and they looked at ours, the ones we used to teach typing, but they thought they were too old. The Germans in their own way were pretty stupid; if you’re being told to collect typewriters, you don’t collect Jews. It sounds like a movie, I know. But it really happened.
经历了战争的种种创伤之后，最不可思议的是，我的童年还算正常。我的父母继续经营着他们的学校——哈格施学习中心（Haagsch Studiehuis），他们在战前和战时就一直在办这所学校，教授打字、速记、语言和商业技能。我在大学期间也曾在那里当过老师。
After all of the trauma of the war, I suppose the amazing thing is that I had a more or less normal childhood. My parents kept running their school—the Haagsch Studiehuis—which they’d done before and during the war, teaching typing, shorthand, languages, and business skills. I too was a teacher there while I was in college.
我的父母热爱艺术，我也从小就接触艺术。大学期间，我的学业和社交生活都非常精彩。1959年我结婚，1960年1月开始读研究生，同年晚些时候，我的第一个女儿宝琳出生。两年后，我的儿子伊曼纽尔（现在叫查克）出生，1965年，我们的第二个女儿艾玛出生。1967年，我们的第二个儿子雅各布在美国出生。
My parents patronized the arts, and I began to learn about art. I had an academically and socially wonderful time in college. I got married in 1959, started graduate school in January 1960, and my first daughter, Pauline, was born later that year. My son Emanuel (who is now called Chuck) was born two years after that, and our second daughter, Emma, came in 1965. Our second son, Jakob, was born in the United States in 1967.
我来到麻省理工学院时，运气不错；我正好置身于当时蓬勃发展的科学发现浪潮之中。尽管我对太空研究一窍不通，但我所拥有的专业知识却与布鲁诺·罗西的开创性X射线天文学团队完美契合。
When I arrived at MIT, luck was on my side; I found myself right in the middle of the explosion of discoveries going on at that time. The expertise I had to offer was perfect for Bruno Rossi’s pioneering X-ray astronomy team, even though I didn’t know anything about space research.
V-2 火箭突破了地球大气层的限制，开辟了全新的探索发现的前景。讽刺的是，V-2火箭的设计者是纳粹分子沃纳·冯·布劳恩。二战期间，他研发这种火箭的目的是为了杀害盟军平民，而这些火箭的破坏力极其巨大。在德国的佩内明德和臭名昭著的米特尔韦克地下工厂，集中营的奴工们制造了这些火箭，约有两万人因此丧生。火箭本身就造成七千多名平民死亡，其中大部分发生在伦敦。在我外公外婆家附近，靠近海牙的地方，有一个发射场，大约一英里远。我记得火箭加注燃料时发出的嘶嘶声，以及发射时的轰鸣声。在一次盟军轰炸中，他们试图摧毁V-2火箭的设备，但却失手炸死了五百名荷兰平民。战后，美国人把冯·布劳恩带到美国，他成了英雄。这始终让我百思不得其解。他可是个战犯啊！
V-2 rockets had broken the bounds of the Earth’s atmosphere, and a whole new vista of opportunity for discoveries had been opened up. Ironically, the V-2 had been designed by Wernher von Braun, who was a Nazi. He developed the rockets during World War II to kill Allied civilians, and they were terribly destructive. In Peenemünde and in the notorious underground Mittelwerk plant in Germany, slave laborers from concentration camps built them, and some twenty thousand died in the process. The rockets themselves killed more than seven thousand civilians, mostly in London. There was a launch site about a mile from my mother’s parents’ house close to The Hague. I recall a sizzling noise as the rockets were being fueled and the roaring noise at launch. In one bombing raid the Allies tried to destroy V-2 equipment, but they missed and killed five hundred Dutch civilians instead. After the war the Americans brought von Braun to the United States and he became a hero. That has always baffled me. He was a war criminal!
冯·布劳恩与美国陆军合作十五年，研制了V-2火箭的后继者——红石和木星导弹，这些导弹都可携带核弹头。1960年，他加入美国国家航空航天局（NASA），担任阿拉巴马州马歇尔太空飞行中心主任，在那里他研发了将宇航员送上月球的土星系列火箭。他的火箭后继者开启了X射线天文学领域，因此，尽管火箭最初是作为武器出现的，但至少它们也被用于大量的科学研究。在20世纪50年代末和60年代初，火箭为我们打开了通往世界——不，是通往宇宙！——的新窗口，让我们有机会窥探地球大气层之外的世界，寻找我们原本无法看到的景象。
For fifteen years von Braun worked with the U.S. Army to build the V-2’s descendants, the Redstone and Jupiter missiles, which carried nuclear warheads. In 1960 he joined NASA and directed the Marshall Space Flight Center in Alabama, where he developed the Saturn rockets that sent astronauts to the Moon. Descendants of his rockets launched the field of X-ray astronomy, so while rockets began as weapons, at least they also got used for a great deal of science. In the late 1950s and early 1960s they opened new windows on the world—no, on the universe!—giving us the chance to peek outside of the Earth’s atmosphere and look around for things we couldn’t see otherwise.
为了发现来自外太空的X射线，罗西凭借直觉做出了决定。1959年，他找到自己的一位名叫马丁·安尼斯（Martin Annis）的学生，安尼斯当时在剑桥一家名为美国科学与工程公司（American Science and Engineering，简称ASE）的研究机构担任负责人。罗西说：“我们不妨看看外太空是否存在X射线。” ASE团队由未来的诺贝尔奖得主里卡多·贾科尼（Riccardo Giacconi）领导，他们将三个盖革-米勒计数器装入一枚火箭，并于1962年6月18日发射升空。火箭在80公里（约50英里）以上的高度停留了六分钟，飞越了地球大气层——这是必要的，因为大气层会吸收X射线。
To discover X-rays from outer space, Rossi had played a hunch. In 1959 he went to an ex-student of his named Martin Annis, who then headed a research firm in Cambridge called American Science and Engineering, and said, “Let’s just see if there are X-rays out there.” The ASE team, headed by future Nobelist Riccardo Giacconi, put three Geiger-Müller counters in a rocket that they launched on June 18, 1962. It spent just six minutes above 80 kilometers (about 50 miles), to get beyond the Earth’s atmosphere—a necessity, since the atmosphere absorbs X-rays.
果然，他们探测到了X射线，更重要的是，他们还确定了X射线来自外部的辐射源。太阳系。这颗重磅炸弹彻底改变了天文学。谁也没想到，谁也想不出它们存在的理由；没人真正理解这一发现。罗西当时只是抱着试试看的态度，抛出一个想法，看看它是否可行。正是这种直觉造就了一位伟大的科学家。
Sure enough, they detected X-rays, and even more important, they were able to establish that the X-rays came from a source outside the solar system. It was a bombshell that changed all of astronomy. No one expected it, and no one could think of plausible reasons why they were there; no one really understood the finding. Rossi had been throwing an idea at the wall to see if it would stick. These are the kinds of hunches that make a great scientist.
我清楚地记得抵达麻省理工学院的确切日期：1966年1月11日。因为我们家一个孩子得了腮腺炎，我们不得不推迟去波士顿的行程；荷兰皇家航空公司不允许我们登机，因为腮腺炎具有传染性。第一天，我就遇到了布鲁诺·罗西和乔治·克拉克。1964年，乔治·克拉克首次驾驶热气球飞到极高海拔——约14万英尺——寻找能够穿透如此高空的高能X射线源。乔治说：“如果你想加入我的团队，那就太好了。” 我真是恰逢其时，出现在了最合适的地方。
I remember the exact date I arrived at MIT, January 11, 1966, because one of our kids got the mumps and we had to delay going to Boston; the KLM wouldn’t let us fly, as the mumps is contagious. On my first day I met Bruno Rossi and also George Clark, who in 1964 had been the first to fly a balloon at a very high altitude—about 140,000 feet—to search for X-ray sources that emitted very high energy X-rays, the kind that could penetrate down to that altitude. George said, “If you want to join my group that would be great.” I was at exactly the right place at the right time.
如果你是第一个做某件事的人，你注定会成功，而我们的团队也确实取得了一系列新的发现。乔治非常慷慨，两年后他就把整个团队完全交给了我。能够站在天体物理学最新浪潮的最前沿，真是太棒了。
If you’re the first to do something, you’re bound to be successful, and our team made one discovery after another. George was very generous; after two years he turned the group completely over to me. To be on the cutting edge of the newest wave in astrophysics was just remarkable.
我当时非常幸运地置身于天体物理学最激动人心的研究工作之中，但事实上，物理学的各个领域都令人惊叹；它们都充满了引人入胜的乐趣，并且不断揭示着惊人的新发现。当我们还在寻找新的X射线源时，粒子物理学家们也在不断发现构成原子核的更多基本单元，解开了原子核的奥秘，发现了传递“弱”核相互作用的W玻色子和Z玻色子，以及传递“强”核相互作用的夸克和胶子。
I was incredibly fortunate to find myself right in the thick of the most exciting work going on in astrophysics at that time, but the truth is that all areas of physics are amazing; all are filled with intriguing delights and are revealing astonishing new discoveries all the time. While we were finding new X-ray sources, particle physicists were finding ever more fundamental building blocks of the nucleus, solving the mystery of what holds nuclei together, discovering the W and Z bosons, which carry the “weak” nuclear interactions, and quarks and gluons, which carry the “strong” interactions.
物理学让我们得以回溯遥远的过去，抵达宇宙的边缘，并拍摄出令人惊叹的哈勃超深空场图像，展现出浩瀚无垠的星系。读完本章，你一定要上网搜索一下哈勃超深空场。我的朋友们甚至把这张图设成了他们的屏保！
Physics has allowed us to see far back in time, to the very edges of the universe, and to make the astonishing image known as the Hubble Ultra Deep Field, revealing what seems an infinity of galaxies. You should not finish this chapter without looking up the Ultra Deep Field online. I have friends who’ve made this image their screen saver!
宇宙的年龄约为137亿年。然而，由于……由于宇宙空间自大爆炸以来已经发生了巨大的膨胀，我们目前观测到的星系形成于大爆炸后约4亿至8亿年，如今它们距离我们已远远超过137亿光年。天文学家现在估计，可观测宇宙的边缘距离我们各个方向约470亿光年。由于空间的膨胀，许多遥远的星系目前正以超过光速的速度远离我们。对于那些从小就接受爱因斯坦狭义相对论“没有任何东西的速度可以超过光速”这一观念的人来说，这听起来或许令人震惊，甚至难以置信。然而，根据爱因斯坦的广义相对论，当空间本身膨胀时，两个星系之间的速度是没有限制的。科学家们现在认为我们正生活在宇宙学的黄金时代——宇宙学是研究整个宇宙起源和演化的学科——这并非没有道理。
The universe is about 13.7 billion years old. However, due to the fact that space itself has expanded enormously since the big bang, we are currently observing galaxies that were formed some 400 to 800 million years after the big bang and that are now considerably farther away than 13.7 billion light-years. Astronomers now estimate that the edge of the observable universe is about 47 billion light-years away from us in every direction. Because of the expansion of space, many faraway galaxies are currently moving away from us faster than the speed of light. This may sound shocking, even impossible, to those of you raised on the notion that, as Einstein postulated in his theory of special relativity, nothing can go faster than the speed of light. However, according to Einstein’s theory of general relativity, there are no limits on the speed between two galaxies when space itself is expanding. There are good reasons why scientists now think that we are living in the golden age of cosmology—the study of the origin and evolution of the entire universe.
物理学解释了彩虹的美丽与脆弱，黑洞的存在，行星的运动规律，恒星爆炸时的现象，花样滑冰运动员收臂时旋转速度加快的原因，宇航员在太空中失重的原因，宇宙中元素的形成，宇宙的起源，长笛的音色，以及我们如何产生驱动身体和经济运转的电力，还有宇宙大爆炸的声音。它描绘了亚原子空间的微观世界和宇宙的遥远角落。
Physics has explained the beauty and fragility of rainbows, the existence of black holes, why the planets move the way they do, what goes on when a star explodes, why a spinning ice skater speeds up when she draws in her arms, why astronauts are weightless in space, how elements were formed in the universe, when our universe began, how a flute makes music, how we generate electricity that drives our bodies as well as our economy, and what the big bang sounded like. It has charted the smallest reaches of subatomic space and the farthest reaches of the universe.
我的朋友兼同事维克多·魏斯科普夫（Victor Weisskopf）在我抵达麻省理工学院时已是位德高望重的学者，他写了一本书，名为《身为物理学家的特权》（The Privilege of Being a Physicist）。这个精彩的书名恰如其分地概括了我身处天文和天体物理学发现史上最激动人心的时期之一的感受——自人类开始认真观测夜空以来，我们一直处于这一时期。我在麻省理工学院的同事们，有时甚至就在我隔壁办公室，设计出了令人惊叹的、极富创造性和精湛的技术，致力于攻克科学中最根本的问题。能够为人类拓展对星辰和宇宙的认知贡献一份力量，我深感荣幸。并让几代年轻人欣赏和热爱这片壮丽的领域。
My friend and colleague Victor Weisskopf, who was already an elder statesman when I arrived at MIT, wrote a book called The Privilege of Being a Physicist. That wonderful title captures the feelings I’ve had being smack in the middle of one of the most exciting periods of astronomical and astrophysical discovery since men and women started looking carefully at the night sky. The people I’ve worked alongside at MIT, sometimes right across the hall from me, have devised astonishingly creative and sophisticated techniques to hammer away at the most fundamental questions in all of science. And it’s been my own privilege both to help extend humankind’s collective knowledge of the stars and the universe and to bring several generations of young people to an appreciation and love for this magnificent field.
自从我小时候把衰变的同位素握在手心以来，我从未停止过对物理学发现的热爱，无论是古老的还是最新的；它丰富的历史和不断拓展的前沿领域；以及它如何让我看到周围世界中那些意想不到的奇妙之处。对我而言，物理学是一种看待事物的方式——它将壮观的和平凡的、宏大的和微小的事物，视为一个美丽而激动人心的整体。
Ever since those early days of holding decaying isotopes in the palm of my hand, I have never ceased to be delighted by the discoveries of physics, both old and new; by its rich history and ever-moving frontiers; and by the way it has opened my eyes to unexpected wonders of the world all around me. For me physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.
我一直以来都努力用这种方式让学生们感受到物理的魅力。我相信，让他们记住科学发现的美妙之处远比专注于复杂的数学计算重要得多——毕竟，他们中的大多数人最终都不会成为物理学家。我竭尽所能地帮助他们以不同的视角看待世界；引导他们提出从未想过的问题；让他们以全新的视角欣赏彩虹；让他们专注于物理学精妙绝伦的美，而不是数学的细枝末节。本书的宗旨也正是如此，它旨在帮助你领略物理学如何以非凡的方式阐明我们世界的运行规律，以及它令人惊叹的优雅与美丽。
That is the way I’ve always tried to make physics come alive for my students. I believe it’s much more important for them to remember the beauty of the discoveries than to focus on the complicated math—after all, most of them aren’t going to become physicists. I have done my utmost to help them see the world in a different way; to ask questions they’ve never thought to ask before; to allow them to see rainbows in a way they have never seen before; and to focus on the exquisite beauty of physics, rather than on the minutiae of the mathematics. That is also the intention of this book, to help open your eyes to the remarkable ways in which physics illuminates the workings of our world and its astonishing elegance and beauty.
第二章
CHAPTER 2
测量、不确定性和恒星
Measurements, Uncertainties, and the Stars
我的祖母和伽利略·伽利莱
My Grandmother and Galileo Galilei
物理学本质上是一门实验科学，测量及其不确定性是所有实验、所有发现的核心。即使是物理学中伟大的理论突破，也是以对可测量物理量的预测形式出现的。例如，牛顿第二定律F = ma （力等于质量乘以加速度），或许是物理学中最重要的一条方程；又如爱因斯坦的E = mc²（能量等于质量乘以光速的平方），物理学中最著名的方程。除了用数学方程来描述密度、重量、长度、电荷、引力、温度或速度等可测量物理量之间的关系之外，物理学家还能用什么其他方式来表达这些关系呢？
Physics is fundamentally an experimental science, and measurements and their uncertainties are at the heart of every experiment, every discovery. Even the great theoretical breakthroughs in physics come in the form of predictions about quantities that can be measured. Take, for example, Newton’s second law, F = ma (force equals mass times acceleration), perhaps the most important single equation in physics, or Einstein’s E = mc2 (energy equals mass times the square of the speed of light), the most renowned equation in physics. How else do physicists express relationships except through mathematical equations about measurable quantities such as density, weight, length, charge, gravitational attraction, temperature, or velocity?
我承认我可能有点偏袒，因为我的博士研究是高精度地测量各种核衰变，而且我在X射线天文学早期所做的贡献来自于对数十个高能X射线源的测量。远在数千光年之外。但没有测量，物理学就无从谈起。同样重要的是，没有不确定性，就没有有意义的测量。
I will admit that I may be a bit biased here, since my PhD research consisted of measuring different kinds of nuclear decay to a high degree of accuracy, and that my contributions in the early years of X-ray astronomy came from my measurements of high-energy X-rays from tens of thousands of light-years away. But there simply is no physics without measurements. And just as important, there are no meaningful measurements without their uncertainties.
你其实一直在不知不觉中依赖着一定程度的不确定性。银行报告你的账户余额时，你预期误差不会超过半美分。网购衣服时，你预期尺码的误差不会超过一个尺码的几分之一。一条34码的裤子，如果误差只有3%，腰围就会变化整整一英寸；它可能变成35码，松松垮垮地挂在你的臀部，也可能变成33码，让你不禁怀疑自己怎么胖了这么多。
You count on reasonable amounts of uncertainty all the time, without realizing it. When your bank reports how much money you have in your account, you expect an uncertainty of less than half a penny. When you buy a piece of clothing online, you expect its fit not to vary more than a very small fraction of a size. A pair of size 34 pants that varies just 3 percent changes a full inch in waist size; it could end up a 35 and hang on your hips, or a 33 and make you wonder how you gained all that weight.
测量结果必须使用正确的单位，这一点至关重要。以耗资1.25亿美元、历时11年的火星气候探测器项目为例，该项目最终因单位混淆而以灾难性结局告终。一个工程团队使用公制单位，而另一个团队使用英制单位，结果导致探测器在1999年9月进入火星大气层，而非进入稳定的轨道。
It’s also vital that measurements are expressed in the right units. Take the case of an eleven-year-long mission costing $125 million—the Mars Climate Orbiter—which came to a catastrophic conclusion because of a confusion in units. One engineering team used metric units while another used English ones, and as a result in September 1999 the spacecraft entered the Martian atmosphere instead of reaching a stable orbit.
本书中我大部分时间都使用公制单位，因为大多数科学家都使用公制单位。但有时，为了方便美国读者，我也会使用英制单位——英寸、英尺、英里和磅。温度方面，我会使用摄氏度或开尔文（摄氏度加273.15）温标，但有时也会使用华氏度，尽管没有物理学家会使用华氏度。
In this book I use metric units most of the time because most scientists use them. From time to time, however, I’ll use English units—inches, feet, miles, and pounds—when it seems appropriate for a U.S. audience. For temperature, I’ll use the Celsius or Kelvin (Celsius plus 273.15) scales but sometimes Fahrenheit, even though no physicist works in degrees Fahrenheit.
我对测量在物理学中至关重要的作用深信不疑，这也是我怀疑那些无法通过测量验证的理论的原因之一。以弦理论，或者说是它的升级版——超弦理论为例，这是理论物理学家们试图构建“万物理论”的最新尝试。尽管弦理论领域不乏杰出的学者，但理论物理学家们至今仍未提出任何实验或预测来检验弦理论的任何命题。弦理论中没有任何内容能够通过实验验证——至少目前如此。这意味着弦理论不具备任何预测能力，这也是为什么一些物理学家，例如哈佛大学的谢尔顿·格拉肖，质疑它是否真的属于物理学范畴。
My appreciation of the crucial role of measurements in physics is one reason I’m skeptical of theories that can’t be verified by means of measurements. Take string theory, or its souped-up cousin superstring theory, the latest effort of theoreticians to come up with a “theory of everything.” Theoretical physicists, and there are some brilliant ones doing string theory, have yet to come up with a single experiment, a single prediction that could test any of string theory’s propositions. Nothing in string theory can be experimentally verified—at least so far. This means that string theory has no predictive power, which is why some physicists, such as Sheldon Glashow at Harvard, question whether it’s even physics at all.
然而，弦理论也有一些才华横溢、雄辩滔滔的拥护者。布莱恩·格林就是其中之一，他的著作和PBS纪录片《优雅的宇宙》（我在片中接受了简短采访）都非常精彩。爱德华·威滕的M理论统一了五种不同的弦理论，并提出存在十一维空间，而我们这些低等生物只能感知到其中的三个维度。这个理论相当奇特，引人深思。
However, string theory has some brilliant and eloquent proponents. Brian Greene is one, and his book and PBS program The Elegant Universe (I’m interviewed briefly on it) are charming and beautiful. Edward Witten’s M-theory, which unified five different string theories and posits that there are eleven dimensions of space, of which we lower-order beings see only three, is pretty wild stuff and is intriguing to contemplate.
但当理论过于离谱时，我就会想起我的外婆，也就是我母亲的母亲，一位非常了不起的女士。她有一些很棒的格言和习惯，展现了她作为科学家的敏锐直觉。比如，她过去常告诉我，站着的时候比躺着的时候矮。我很喜欢把这个道理教给我的学生。开学第一天，我就会告诉他们，为了纪念我的外婆，我要把这个看似荒谬的观点运用到考试中。他们当然会一头雾水。我仿佛能看到他们在想：“站着比躺着矮？这怎么可能！”
But when theory gets way out there, I am reminded of my grandmother, my mother’s mother, a very great lady who had some wonderful sayings and habits that showed her to be quite an intuitive scientist. She used to tell me, for instance, that you are shorter when standing up than when lying down. I love to teach my students about this. On the first day of class I announce to them that in honor of my grandmother, I’m going to bring this outlandish notion to a test. They, of course, are completely bewildered. I can almost see them thinking, “Shorter standing up than lying down? Impossible!”
他们的怀疑是可以理解的。如果躺着和站着时身高真的有差别，那差别肯定很小。毕竟，如果差了一英尺，你肯定能感觉到，不是吗？你早上起床，站起来，就会“咚”的一声——你矮了一英尺。但如果差别只有0.1厘米（1/25英寸），你可能永远都不会察觉。所以我怀疑，如果我奶奶说的是真的，那么差别可能只有几厘米，也许也就一英寸左右。
Their disbelief is understandable. Certainly if there is any difference in length between lying down and standing up it must be quite small. After all, if it was one foot, you’d know it, wouldn’t you? You’d get out of bed in the morning, you’d stand up and go clunk—you’re one foot shorter. But if the difference was only 0.1 centimeters (1/25 of an inch) you might never know. That’s why I suspect that if my grandmother was right, then the difference is probably only a few centimeters, maybe as much as an inch.
为了进行实验，我首先当然需要让他们相信我的测量结果存在不确定性。所以我先测量一根铝棒的垂直长度——结果是 150.0 厘米——然后请他们确认我的测量误差大概在正负十分之一厘米以内。所以，垂直测量结果为 150.0 ± 0.1 厘米。接着，我测量铝棒水平放置时的长度，结果是 149.9 ± 0.1 厘米，这个结果与垂直测量结果一致——在测量误差范围内。
To conduct my experiment, I of course first need to convince them of the uncertainty in my measurements. So I begin by measuring an aluminum rod vertically—it comes to 150.0 centimeters—and I ask them to agree that I’m probably capable of measuring it with an uncertainty of plus or minus one-tenth of a centimeter. So that vertical measurement is 150.0 ± 0.1 centimeters. I then measure the bar when it’s horizontal and come up with 149.9 ± 0.1 centimeters, which is in agreement—within the uncertainty of the measurements—with the vertical measurement.
通过测量铝棒在两种不同位置的重量，我获得了什么？很多！首先，这两个测量结果表明我能够……测量长度的精度约为0.1厘米（1毫米）。但对我来说，更重要的是，我想向学生们证明我没有在和他们开玩笑。例如，假设我特意准备了一根“煮熟的”米尺来进行水平测量——那将是一种极其恶劣、极其不诚实的行为。通过证明两次测量中铝棒的长度相同，我就能证明我的科学诚信毋庸置疑。
What did I gain by measuring the aluminum rod in both positions? A lot! For one, the two measurements demonstrate that I was able to measure length to an accuracy of about 0.1 centimeter (1 millimeter). But at least as important for me is the fact that I want to prove to the students that I’m not playing games with them. Suppose, for example, that I have prepared a specially “cooked” meter stick for my horizontal measurements—that would be a terrible, very dishonest thing to do. By showing that the length of the aluminum rod is the same in the two measurements, I establish that my scientific integrity is beyond doubt.
然后我找了一位志愿者，让他站着量身高，把数字写在黑板上——185.2厘米（略多于6英尺），当然，误差在正负0.1厘米以内。接着我帮他躺在我的桌子上，用我的测量设备测量身高。这设备看起来像个巨大的丽兹尺，就是鞋店里那种木制的量脚器，只不过他的整个身体就是那只尺子。我跟他开玩笑说他感觉很舒服，还祝贺他为了科学做出了牺牲，这让他有点不安。我还有什么妙招呢？我把那个三角形的木块紧紧地贴在他的头上，趁他躺着的时候，把新的数字写在黑板上。这样我们就有了两个测量结果，每个结果的误差都在0.1厘米左右。结果是什么呢？
I then ask for a volunteer, measure him standing up, write that number on the blackboard—185.2 centimeters (or just over 6 feet), plus or minus 0.1 centimeter of course, to account for the uncertainty. Then I help him lie down on my desk in my measuring equipment, which looks like a giant Ritz Stick, the wooden shoe-store foot-measuring device, only his whole body is the foot. I joke back and forth with him about how comfortable he is and congratulate him on his sacrifice for the sake of science, which makes him just a wee bit uneasy. What have I got up my sleeve? I slide the triangular wooden block snug up against his head, and while he lies there, I write the new number on the board. So we now have two measurements, each uncertain by about 0.1 centimeters. What’s the result?
得知这两个测量结果相差2.5厘米（当然，误差在正负0.2厘米以内），你是不是很惊讶？我不得不得出结论：他躺着的时候实际上至少比站着的时候高2.3厘米（约0.9英寸）。我回到躺着的学生身边，宣布他睡觉时比站着时高出大约一英寸，然后——这才是最精彩的部分——我宣布：“我奶奶说得对！她总是对的！”
Are you surprised to learn that the two measurements differ by 2.5 centimeters, plus or minus 0.2 centimeters of course? I have to conclude that he is in fact at least 2.3 centimeters (or about 0.9 inches) taller while lying down. I go back to my prone student, announce that he’s roughly an inch taller sleeping than standing up, and—this is the best part—declare, “My grandmother was right! She was always right!”
你对此表示怀疑吗？好吧，事实证明，我的祖母比我们大多数人都更懂科学。当我们站立时，重力会挤压脊椎骨之间的软组织；当我们躺下时，脊椎会伸展。一旦你了解了这一点，它似乎就显而易见了，但你能预料到吗？事实上，即使是美国宇航局（NASA）的科学家在规划最初的太空任务时也没有预料到这种效应。宇航员们抱怨说，他们在太空中的宇航服会变得更紧。后来在天空实验室任务期间进行的研究表明……接受测量的六名宇航员身高均增长了约3%——如果你身高6英尺（约1.83米），那就相当于长高了2英寸（约5厘米）。现在宇航员的宇航服都预留了额外的空间，以适应宇航员的这种身高增长。
Are you skeptical? Well, it turns out that my grandmother was a better scientist than most of us. When we are standing, the tug of gravity compresses the soft tissue between the vertebrae of our spines, and when we lie down, our spines expand. This may seem obvious once you know it, but would you have predicted it? In fact, not even the scientists at NASA anticipated this effect in planning the first space missions. The astronauts complained that their suits got tighter when they were in space. Studies done later, during the Skylab mission, showed that of the six astronauts who were measured, all six showed about 3 percent growth in height—a little over 2 inches if you’re 6 feet tall. Now astronauts’ suits are made with extra room to allow for this growth.
你看，精准的测量能揭示多少真相？就在我证明祖母观点正确的那堂课上，我饶有兴致地测量了一些非常奇特的物品，这一切都是为了验证伟大的伽利略·伽利莱——现代科学和天文学之父——提出的一个观点。他曾问自己：“为什么最大的哺乳动物体型如此之大，而不是更大？”他给出的答案是：如果哺乳动物的体重过重，它们的骨骼就会断裂。当我读到这段文字时，我很好奇他的观点是否正确。他的答案似乎很有道理，但我还是想验证一下。
See how revealing good measurements can be? In that same class where I prove my grandmother right, I have a lot of fun measuring some very odd items, all in order to test a suggestion of the great Galileo Galilei, the father of modern science and astronomy, who once asked himself the question, “Why are the largest mammals as large as they are and not much larger?” He answered himself by suggesting that if a mammal became too heavy, its bones would break. When I read about this, I was intrigued to find out whether or not he was right. His answer seemed right intuitively, but I wanted to check it.
我知道哺乳动物的股骨（也就是大腿骨）支撑着它们的大部分体重，所以我决定对不同哺乳动物的股骨进行一些对比测量。如果伽利略的说法是正确的，那么对于体型非常大的哺乳动物来说，股骨的强度可能不足以支撑它们的体重。当然，我也意识到哺乳动物股骨的强度应该取决于它的粗细。更粗的骨头可以承受更大的重量——这很直观。动物体型越大，它们的骨骼就需要越强壮。
I knew that mammals’ femurs—their thighbones—support most of their weight, so I decided to make some comparative measurements of different mammals’ femur bones. If Galileo was right, then for a super heavy mammal, the femur bone would not be strong enough to support the animal. Of course, I realized that the strength of the mammal’s femur should depend on its thickness. Thicker bones can support more weight—that’s intuitive. The bigger the animal, the stronger the bones would need to be.
当然，随着动物体型增大，股骨也会变长。我意识到，通过比较不同哺乳动物股骨长度和粗度随体型增大而增加的幅度，我可以验证伽利略的观点。根据我所做的计算（计算过程比这里要复杂得多，我在附录1中详细解释），我得出结论：如果伽利略的观点正确，那么随着哺乳动物体型增大，其股骨的粗度必须比长度增长得更快。例如，我计算得出，如果一种动物的体型是另一种动物的五倍——也就是说，它的股骨长度是后者的五倍——那么它的股骨粗度就必须大约是后者的十一倍。
The femur would also get longer as the animal got bigger, of course, and I realized that by comparing how much longer versus how much thicker the femurs of various mammals get as the animals become bigger, I could test Galileo’s idea. According to the calculations I made, which are more complicated than I want to go into here (I explain them in appendix 1), I determined that if Galileo was right, then as mammals get bigger the thickness of their femurs would have to increase faster than their length. I calculated that, for example, if one animal was five times bigger than another—so the femur would be five times longer—then the thickness of its femur would have to be about eleven times greater.
这意味着，在某个阶段，股骨的粗细会与长度相等，甚至更长，这将造就一些非常不切实际的哺乳动物。这样的动物当然会……可能并非最适应生存的物种，而这正是哺乳动物体型存在最大限制的原因。
This would mean that at some point the thicknesses of femurs would become the same as their lengths—or even greater—which would make for some pretty impractical mammals. Such an animal would certainly not be the fittest for survival, and that would then be the reason why there is a maximum limit on the size of mammals.
所以，我的预测没错，厚度增长速度会比长度增长速度快。现在，真正的乐趣开始了。
So, I had my prediction that thickness would increase faster than length. Now the real fun began.
我去了哈佛大学，那里收藏着非常精美的骨骼标本。我向他们索要了浣熊和马的股骨。结果发现，马的体型大约是浣熊的四倍，而且马的股骨（42.0 ± 0.5 厘米）长度也确实比浣熊的股骨（12.4 ± 0.3 厘米）长了大约三倍半。到目前为止，一切都很顺利。我把这些数据代入公式，预测马的股骨厚度应该是浣熊股骨的六倍多一点。当我测量股骨厚度时（浣熊股骨的误差约为半厘米，马股骨的误差约为两厘米），结果发现马的股骨厚度是浣熊股骨的五倍，误差约为百分之十。所以，伽利略的理论看起来非常正确。然而，我决定扩大数据范围，将体型更小和更大的哺乳动物都纳入其中。
I went over to Harvard University, where they have a beautiful collection of bones, and I asked them for the femurs of a raccoon and a horse. It turns out that a horse is about four times larger than a raccoon, and sure enough, the horse’s femur (42.0 ± 0.5 centimeters) was about three and a half times longer than the raccoon’s (12.4 ± 0.3 centimeters). So far so good. I plugged the numbers into my formula and predicted that the horse’s femur should be a little more than six times thicker than the raccoon’s. When I measured the thicknesses (to an uncertainty of about half a centimeter for the raccoon and 2 centimeters for the horse), it turned out that the horse bone was five times thicker, plus or minus about 10 percent. So it looked very good for Galileo. However, I decided to expand the data to include smaller as well as larger mammals.
于是我又回到哈佛，他们又给了我三根骨头，分别是羚羊的、负鼠的和老鼠的。以下是它们的对比情况：
So I went back to Harvard, and they gave me three more bones, of an antelope, an opossum, and a mouse. Here’s how they all stacked up:
多么美妙，多么浪漫啊！形状的演变如此动人，瞧瞧老鼠的股骨多么纤细、多么小巧。对于一只如此娇小的老鼠来说，这股骨也真是小得可怜。多么美丽啊！我永远都会为自然界每一个细节的美丽而惊叹不已。
Isn’t that wonderful, so romantic? The progression of shapes is lovely, and look at how delicate, how tiny is the femur of the mouse. Only a teeny weenie little femur for a teeny, weenie little mouse. Isn’t that beautiful? I will never cease to be amazed by the beauty in every detail of our natural world.
但是测量数据呢？它们如何与我的公式相符？当我进行计算时，我震惊了，真的震惊了。马的股骨长度大约是老鼠的40倍，我的计算结果预测它的股骨厚度应该是老鼠的250倍以上。然而，实际情况却只有大约70倍厚。
But what about the measurements; how did they fit into my equation? When I did the calculations, I was shocked, really shocked. The horse femur is about 40 times longer than the mouse’s, and my calculations predicted that its femur should be more than 250 times thicker. Instead, it was only about 70 times thicker.
于是我心想：“我为什么不向他们要一根象腿骨呢？那样或许就能彻底解决这个问题了。” 我想当我再次回到哈佛时，他们有点不高兴，但他们还是好心地给了我一根象腿骨。那时候我敢肯定，他们只想赶紧打发我走！相信我，扛着那根骨头可真够费劲的；它超过一码长，重得像一吨。我迫不及待地想测量尺寸；为此我整夜都没睡着。
So I said to myself, “Why didn’t I ask them for the femur of an elephant? That might settle the issue conclusively.” I think they were somewhat annoyed at Harvard when I came back again, but they kindly gave me the femur of an elephant. By that time I’m sure they just wanted to get rid of me! Believe me, it was difficult carrying that bone; it was more than a yard long and weighed a ton. I couldn’t wait to do my measurements; I couldn’t sleep all night.
你知道我发现了什么吗？老鼠的股骨长1.1±0.05厘米，厚0.7±0.1毫米——确实非常细。大象的股骨长101±1厘米，大约是老鼠股骨的100倍。那么它的厚度呢？我测量出的厚度为86±4毫米，大约是老鼠股骨直径的120倍。但根据我的计算，如果伽利略的说法是正确的，那么大象的股骨应该比老鼠的股骨厚约1000倍。换句话说，它的厚度应该约为70厘米。然而，实际的厚度只有大约9厘米。尽管很不情愿，但我不得不得出结论：伟大的伽利略·伽利莱错了！
And do you know what I found? The mouse’s femur was 1.1 ± 0.05 centimeters long and 0.7 ± 0.1 millimeters thick—very thin indeed. The elephant’s femur was 101 ± 1 centimeters long, about 100 times longer than that of the mouse. So how about its thickness? I measured it at 86 ± 4 millimeters, roughly 120 times the diameter of the mouse’s femur. But according to my calculations, if Galileo was right, the femur of the elephant should be roughly 1,000 times thicker than that of the mouse. In other words, it should have been about 70 centimeters thick. Instead, the actual thickness was only about 9 centimeters. I concluded, however reluctantly, that the great Galileo Galilei was wrong!
测量星际空间
Measuring Interstellar Space
在物理学领域，测量一直令天文学备受困扰。测量及其不确定性对天文学家来说是极其棘手的问题，尤其因为我们面对的是极其遥远的距离。星星离我们有多远？我们美丽的邻居——仙女座星系呢？我们用最强大的望远镜能看到的所有星系又有多远？当我们看到宇宙中最遥远的物体时，我们看到的究竟有多远？宇宙究竟有多大？
One of the areas of physics in which measurement has been bedeviling is astronomy. Measurements and uncertainties are enormous issues for astronomers, especially because we deal with such immense distances. How far away are the stars? How about our beautiful neighbor, the Andromeda Galaxy? And what about all the galaxies we can see with the most powerful telescopes? When we see the most-distant objects in space, how far are we seeing? How large is the universe?
这些都是科学中最根本、最深刻的问题。而不同的答案彻底颠覆了我们对宇宙的认知。事实上，距离的计算有着一段精彩的历史。你可以通过恒星距离计算技术的演变来追溯天文学自身的发展历程。而每个阶段的计算都取决于测量的精确度，也就是仪器的精度和天文学家的创造力。直到19世纪末，天文学家进行这些计算的唯一方法是测量一种叫做视差的现象。
These are some of the most fundamental and profound questions in all of science. And the different answers have turned our view of the universe upside down. In fact, the whole distance business has a wonderful history. You can trace the evolution of astronomy itself through the changing techniques of calculating stellar distances. And at every stage these are dependent on the degree of accuracy of measurements, which is to say the equipment and the inventiveness of astronomers. Until the end of the nineteenth century, the only way astronomers could make these calculations was by measuring something called parallax.
你们可能都熟悉视差现象，只是自己没有意识到而已。无论你坐在哪里，环顾四周，找到一段墙，墙上有一些物体——比如门或挂在上面的画——或者如果你在户外，可以找一些景观中的物体，比如一棵大树。现在，伸出你的手，竖起一根手指，让它指向那个物体的一侧或另一侧。先闭上右眼，再闭上左眼。你会发现，相对于门或树，你的手指从左向右跳动了一下。现在，把手指靠近眼睛，再重复一遍。你会发现手指的移动幅度更大。效果非常显著！这就是视差。
You are all familiar with the phenomenon of parallax without even realizing it. Wherever you are sitting, look around and find a stretch of wall with some sort of feature along it—a doorway or a picture hanging on it—or if you’re outside some feature of the landscape, like a big tree. Now stretch your hand straight out in front of you and raise one finger so that it is to one or the other side of that feature. Now first close your right eye and then close your left eye. You will see that your finger jumped from left to right relative to the doorway or the tree. Now, move your finger closer to your eyes and do it again. Your finger moves even more. The effect is huge! This is parallax.
这是由于观察物体时视线方向的改变造成的，在这种情况下，视线方向是从左眼切换到右眼（你的眼睛相距约 6.5 厘米）。
It happens because of the switch to different lines of sight in observing an object, so in this case from the line of sight of your left eye to that of your right eye (your eyes are about 6.5 centimeters apart).
这就是测定恒星距离的基本原理。只不过，我们不再以我双眼约6.5厘米的间距作为基准，而是以地球轨道直径（约3亿公里）作为基准。地球绕太阳公转一周（轨道直径约为3亿公里），一年内，一颗近处的恒星相对于更遥远的恒星在天空中的位置会发生移动。我们测量的是天空中两颗恒星之间的夹角（称为视差角）。两次测量恒星的位置，两次测量间隔六个月。如果进行多组测量，每次间隔六个月，就会发现不同的视差角。为了简化说明，下图选取了一颗与地球位于同一空间平面（称为轨道平面，也称黄道面）上的恒星。然而，这里描述的视差测量原理适用于任何恒星，而不仅仅是黄道面上的恒星。
This is the basic idea behind determining distances to stars. Except that instead of the approximately 6.5 centimeters separation of my eyes as our baseline, we now use the diameter of the Earth’s orbit (about 300 million kilometers) as our baseline. As the Earth moves around the Sun in one year (in an orbit with a diameter of about 300 million kilometers) a nearby star will move in the sky relative to more distant stars. We measure the angle in the sky (called a parallax angle) between the two positions of the star measured six months apart. If you make many sets of measurements all six months apart, you will find different parallax angles. In the figure below, for simplicity, I have selected a star in the same plane of space as Earth, known as the orbital plane (also called the ecliptic plane). However, the principle of parallax measurements as described here holds for any star—not just for stars in the ecliptic plane.
假设地球位于绕太阳公转轨道上的位置 1 时观测这颗恒星。此时，你会看到这颗恒星在背景（非常遥远）上的投影方向为 A1。六个月后（从位置 7）再次观测同一颗恒星，你会看到它位于 A7 方向。标记为α 的角度是最大可能的视差角。如果你从位置 2 和 8、3 和 9、4 和 10 进行类似的测量，你会发现视差角总是小于α。假设从位置 4 和 10 进行观测（假设情况如此，因为此时太阳会遮挡视线，无法从位置 10 观测到这颗恒星），视差角甚至会为零。现在观察由点 1、A 和 7 构成的三角形。我们知道点 1 到 7 的距离是 3 亿公里，并且我们知道角度α 。因此，我们现在可以用高中数学知识计算出距离SA 。
Suppose you observe the star when the Earth is located at position 1 in its orbit around the Sun. You will then see the star projected on the background (very far away) in the direction A1. If now you observe the same star six months later (from position 7), you will see the star in the direction A7. The angle marked as α is the largest possible parallax angle. If you make similar measurements from positions 2 and 8, 3 and 9, 4 and 10, you will then always find parallax angles that are smaller than α. In the hypothetical case of observations from points 4 and 10 (hypothetical, as the star cannot be observed from position 10 since the Sun is then in the way), the parallax angle would even be zero. Now look at the triangle that is formed by the points 1A7. We know that the distance 1–7 is 300 million kilometers, and we know the angle α. Thus we can now calculate the distance SA (with high school math).
尽管每隔六个月测量的视差角各不相同，天文学家仍然讨论恒星的视差。他们所说的视差是指最大视差角的一半。如果最大视差角为 2.00 角秒，那么视差就是 1.00 角秒，恒星的距离就是 3.26 光年（然而，实际情况可能并非如此）。（没有离我们这么近的恒星）。视差越小，距离越远。如果视差为 0.10 角秒，则其距离为 32.6 光年。离太阳最近的恒星是比邻星。它的视差为 0.76 角秒；因此，它距离我们约 4.3 光年。
Even though the parallax angles taken at different six-month intervals vary, astronomers talk about the parallax of a star. What they mean by that is half the largest parallax angle. If the maximum parallax angle was 2.00 arc seconds, then the parallax would be 1.00 arc seconds and the distance to the star would then be 3.26 light-years (however, there is no star that close to us). The smaller the parallax, the greater the distance. If the parallax is 0.10 arc seconds, its distance is 32.6 light-years. The star nearest the Sun is Proxima Centauri. Its parallax is 0.76 arc seconds; thus its distance is about 4.3 light-years.
为了理解天文学家必须测量的恒星位置变化究竟有多小，我们首先需要了解一角秒究竟有多小。想象一下，在夜空中画一个巨大的圆，它穿过天顶（正上方），环绕地球一周。这个圆当然包含360度。现在，每度又被分成60角分，每角分又被分成60角秒。因此，这个完整的圆共有1,296,000角秒。由此可见，一角秒极其微小。
To understand just how small the changes in stellar positions are that astronomers must measure, we have to understand just how small an arc second is. Picture an enormous circle drawn in the night sky going through the zenith (which is straight overhead) all the way around the Earth. That circle of course contains 360 degrees. Now each degree is divided into 60 arc minutes, and each arc minute is divided in turn into 60 arc seconds. So there are 1,296,000 arc seconds in that full circle. You can see that an arc second is extremely small.
另一种理解它有多小的方法。如果你拿一枚一角硬币，把它移到离你2.2英里远的地方，它的直径就是一角秒。再举一个例子。每个天文学家都知道，月球的直径大约是半度，也就是30角分。这被称为月球的角大小。如果你能把月球切成1800片等薄的薄片，每一片的宽度也都是一角秒。
Here’s another way to envision how small. If you take a dime and move it 2.2 miles away from you, its diameter would be one arc second. And here’s another. Every astronomer knows that the Moon is about half a degree across, or 30 arc minutes. This is called the angular size of the Moon. If you could cut the Moon into 1,800 equally thin slices, each one would be an arc second wide.
由于天文学家为了确定距离而必须测量的视差角非常小，因此您应该能够理解测量的不确定性程度对他们来说有多么重要。
Since the parallax angles that astronomers must measure in order to determine distances are so very small, you may appreciate how important the degree of uncertainty in the measurements is for them.
随着仪器设备的改进，天文学家能够进行越来越精确的测量，他们对恒星距离的估计也随之改变，有时甚至发生显著变化。19世纪初，托马斯·亨德森测量了天空中最亮的恒星——天狼星的视差，结果为0.23角秒，不确定度约为0.25角秒。换句话说，他测得的视差上限约为0.5角秒，这意味着这颗恒星距离我们最近的距离为6.5光年。在1839年，这是一个非常重要的结果。但半个世纪后，大卫·吉尔测量出天狼星的视差为0.370角秒，不确定度为±0.010角秒。吉尔的测量结果与亨德森的测量结果一致，但吉尔的测量结果更为精确，因为其不确定度比亨德森小了25倍。视差为 0.370 ± 0.010 角秒，天狼星的距离变为 8.81 ± 0.23 光年，这确实大于 6.5 光年！
As improvements in equipment have allowed astronomers to make more and more accurate measurements, their estimates of stellar distances have changed, sometimes quite dramatically. In the early nineteenth century Thomas Henderson measured the parallax of the brightest star in the heavens, Sirius, to be 0.23 arc seconds, with an uncertainty of about a quarter of an arc second. In other words, he had measured an upper limit for the parallax of about half an arc second, and that meant that the star could not be closer to us than 6.5 light-years. In 1839 this was a very important result. But a half century later, David Gill measured Sirius’s parallax at 0.370 arc seconds with an uncertainty of plus or minus 0.010 arc seconds. Gill’s measurements were consistent with Henderson’s, but Gill’s measurements were highly superior because the uncertainty was twenty-five times smaller. At a parallax of 0.370 ± 0.010 arc seconds, the distance to Sirius becomes 8.81 ± 0.23 light-years, which is indeed larger than 6.5 light-years!
上世纪90年代，高精度视差收集卫星依巴谷（Hipparcos，我记得他们反复修改名字，最终才和一位古希腊著名天文学家的名字相符）测量了超过十万颗恒星的视差（从而计算出它们的距离），误差仅为千分之一角秒左右。这难道不令人难以置信吗？想想看，一枚一角硬币要代表一角秒的距离有多远？要覆盖千分之一角秒的范围，它必须距离观测者2200英里。
In the 1990s Hipparcos, the High Precision Parallax Collecting Satellite (I think they fiddled with the name until it matched the name of a famous ancient Greek astronomer), measured the parallaxes of (and hence the distances to) more than a hundred thousand stars with an uncertainty of only about a thousandth of an arc second. Isn’t that incredible? Remember how far away that dime had to be to represent an arc second? To cover a thousandth of an arc second, it would have to be 2,200 miles away from an observer.
依巴谷卫星测量视差的恒星之一当然是天狼星，结果为 0.37921 ± 0.00158 角秒。由此得出天狼星的距离为 8.601 ± 0.036 光年。
One of the stars Hipparcos measured the parallax of was, of course, Sirius, and the result was 0.37921 ± 0.00158 arc seconds. This gives a distance to Sirius of 8.601 ± 0.036 light-years.
迄今为止最精确的视差测量是由射电天文学家在1995年至1998年间对一颗名为天蝎座X-1的特殊恒星进行的。我将在第十章详细介绍。他们测得的视差为0.00036±0.00004角秒，换算成距离为9.1±0.9千光年。
By far the most accurate parallax measurement ever made was by radio astronomers during the years 1995 to 1998 for a very very special star called Sco X-1. I will tell you all about it in chapter 10. They measured a parallax of 0.00036 ± 0.00004 arc seconds, which translates into a distance of 9.1 ± 0.9 thousand light-years.
除了天文学中由于设备精度有限以及观测时间受限而必须面对的不确定性之外，还有天文学家们最害怕的“未知隐患”。你是否可能因为遗漏了某些信息，或者因为仪器校准错误而犯下自己都不知道的错误？假设你的体重秤设定为10磅时归零，而且自购买以来一直如此。直到你去看医生时才发现这个错误——差点吓得心脏病发作。我们称之为系统误差，它让我们感到无比恐惧。我并不喜欢前国防部长唐纳德·拉姆斯菲尔德，但当他在2002年的一次新闻发布会上说：“我们知道有些事情我们不知道。但还有一些我们不知道自己不知道的未知。” 这句话让我略感同情。
In addition to the uncertainties that we must deal with in astronomy as a consequence of the limited accuracy of our equipment, and also to limits in available observation time, there are the astronomers’ nightmares: the “unknown-hidden” uncertainties. Is there perhaps an error you are making that you don’t even know about because you’re missing something, or because your instruments are calibrated incorrectly? Suppose your bathroom scale is set to show zero at 10 pounds and has been that way since you bought it. You only discover the error when you go to the doctor—and nearly have a heart attack. We call that a systematic error, and it scares the hell out of us. I’m no fan of former secretary of defense Donald Rumsfeld, but I did feel a tiny bit of sympathy when he said, in a 2002 press briefing, “We know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know.”
我们设备性能的局限性带来的挑战，使得一位才华横溢却鲜为人知的女天文学家亨丽埃塔·斯旺的成就显得尤为珍贵。更令人惊叹的是，勒维特在1908年还在哈佛天文台担任低级职员时就开始了这项工作，这项工作使得测量恒星距离取得了巨大的飞跃。
The challenges of the limits of our equipment make the achievement of one brilliant but mostly ignored female astronomer, Henrietta Swan Leavitt, all the more astonishing. Leavitt was working at the Harvard Observatory in a low-level staff position in 1908 when she started this work, which enabled a giant jump in measuring the distance to stars.
这种事情在科学史上屡见不鲜，应该被视为一种系统性错误：低估了女科学家的才华、智慧和贡献。*
This kind of thing has happened so often in the history of science that it should be considered a systematic error: discounting the talent, intellect, and contributions of female scientists.*
莱维特在分析数千张小麦哲伦星云（SMC）的底片时注意到，对于一类大型脉动星（现在被称为造父变星），恒星的光学亮度与其完成一次完整脉动所需的时间（称为恒星周期）之间存在某种关系。她发现周期越长，恒星就越亮。正如我们将看到的，这一发现为精确测量星团和星系的距离打开了大门。
Leavitt noticed, in the course of her job analyzing thousands of photographic plates of the Small Magellanic Cloud (SMC), that with a certain class of large pulsating stars (now known as Cepheid variables), there was a relationship between the star’s optical brightness and the time it took for one complete pulsation, known as the star’s period. She found that the longer the period, the brighter the star. As we will see, this discovery opened the door to accurately measuring distances to star clusters and galaxies.
要理解这项发现，我们首先必须了解亮度和光度的区别。光学亮度是指地球上每平方米每秒接收到的光的能量，它是用光学望远镜测量的。而光学光度则是指天体每秒辐射出的能量。
To appreciate the discovery, we first must understand the difference between brightness and luminosity. Optical brightness is the amount of energy per square meter per second of light we receive on Earth. This is measured using optical telescopes. Optical luminosity, on the other hand, is the amount of energy per second radiated by an astronomical object.
以金星为例，它通常是夜空中最亮的星体，甚至比天空中最亮的恒星天狼星还要亮。金星距离地球非常近，因此非常明亮，但它本身的辐射亮度几乎可以忽略不计。与天狼星相比，金星辐射的能量相对较少。天狼星是一颗能量强大的核燃烧熔炉，质量是太阳的两倍，亮度大约是太阳的25倍。了解一个天体的亮度能让天文学家了解很多关于它的信息，但亮度的难点在于，过去一直没有有效的测量方法。亮度之所以能被测量，是因为它是肉眼可见的；而亮度本身却无法直接测量。要测量亮度，必须同时知道恒星的亮度和距离。
Take Venus, often the brightest object in the entire night sky, even brighter than Sirius, which is the brightest star in the sky. Venus is very close to Earth; it’s therefore very bright, but it has virtually no intrinsic luminosity. It radiates relatively little energy by comparison to Sirius, a powerful, nuclear-burning furnace twice as massive as our Sun and about twenty-five times as luminous. Knowing an object’s luminosity tells astronomers a great deal about it, but the tricky thing about luminosity was that there was no good way to measure it. Brightness is what you measure because it’s what you can see; you can’t measure luminosity. To measure luminosity you have to know both the star’s brightness and its distance.
利用一种名为统计视差的技术，埃纳尔·赫茨普龙（Ejnar Hertzsprung）于1913年，哈洛·沙普利（Harlow Shapley）于1918年，成功地将勒维特的亮度值转换为光度。他们假设在小麦哲伦星云（SMC）中，同一周期造父变星的光度与其他周期相同的造父变星的光度相同，从而计算出所有造父变星（甚至包括SMC以外的造父变星）的光度关系。这里我不打算详细阐述这种方法，因为它相当复杂；重要的是要理解，确定光度-周期关系是距离测量史上的一个里程碑。一旦知道了恒星的光度和亮度，就可以计算出它的距离。
Using a technique called statistical parallax, Ejnar Hertzsprung, in 1913, and Harlow Shapley, in 1918, were able to convert Leavitt’s brightness values into luminosities. And by assuming that the luminosity of a Cepheid with a given period in the SMC was the same as that of a Cepheid with the same period elsewhere, they had a way to calculate the luminosity relationship for all Cepheids (even those outside the SMC). I won’t elaborate here on this method, as it gets quite technical; the important thing to appreciate is that working out the luminosity-period relation was a milestone in measurements of distances. Once you know a star’s luminosity and its brightness, you can calculate its distance.
顺便一提，它们的亮度变化范围相当大。周期为三天的造父变星的亮度约为太阳的1000倍。而当它的周期为30天时，其亮度则约为太阳的13000倍。
The range in luminosity, by the way, is substantial. A Cepheid with a period of three days has about a thousand times the Sun’s luminosity. When its period is thirty days, its luminosity is about thirteen thousand times greater than the Sun’s.
1923年，伟大的天文学家埃德温·哈勃在仙女座星系（也称M31）中发现了造父变星，并据此计算出其距离约为100万光年。这一结果令许多天文学家震惊不已。包括沙普利在内的许多人都认为，我们所在的银河系包含了整个宇宙，包括M31。而哈勃的发现表明，事实上，M31距离我们几乎难以想象。但是等等——如果你用谷歌搜索仙女座星系的距离，你会发现它其实距离我们250万光年。
In 1923, the great astronomer Edwin Hubble found Cepheids in the Andromeda Galaxy (also known as M31), from which he calculated its distance at about 1 million light-years, a genuinely shocking result to many astronomers. Many, including Shapley, had argued that our own Milky Way contained the entire universe, including M31, and Hubble demonstrated that in fact it was almost unimaginably distant from us. But wait—if you google the distance to the Andromeda Galaxy, you’ll find that it’s 2.5 million light-years.
这是一起“未知未知”的案例。尽管哈勃才华横溢，但他还是犯了一个系统性错误。他原本以后来被称为II型造父变星的已知光度为基础进行计算，而实际上他观测到的是一种光度大约是他所认为的II型造父变星四倍的造父变星（这些后来被命名为I型造父变星）。天文学家直到20世纪50年代才发现这一差异，一夜之间，他们意识到过去三十年来的距离测量结果存在两倍的误差——如此巨大的系统性误差使得已知宇宙的大小翻了一番。
This was a case of unknown unknowns. For all his genius, Hubble had made a systematic error. He had based his calculations on the known luminosity of what later came to be known as Type II Cepheids, when in fact he was observing a kind of Cepheid variable about four times more luminous than what he thought he was seeing (these were later named Type I Cepheids). Astronomers only discovered the difference in the 1950s, and overnight they realized that their distance measurements for the previous thirty years were off by a factor of two—a large systematic error that doubled the size of the known universe.
2004 年，天文学家仍然使用造父变星法测量了仙女座星系的距离，结果为 251 ± 13 万光年。2005年，另一组科学家利用食双星法对其进行了测量，结果为252±14万光年，约合1500万亿英里。这两个测量结果非常吻合。然而，误差却高达约14万光年（约8×10¹⁷英里）。而从天文尺度来看，这颗星系已经算是我们的近邻了。试想一下，我们对其他众多星系的距离又该有多么不确定呢？
In 2004, still using the Cepheid variable method, astronomers measured the distance to the Andromeda Galaxy at 2.51 ± 0.13 million lightyears. In 2005 another group measured it by using the eclipsing binary stars method, to get a result of 2.52 ± 0.14 million light-years, about 15 million trillion miles. These two measurements are in excellent agreement with each other. Yet the uncertainty is about 140,000 light-years (about 8 × 1017 miles). And this galaxy is by astronomical standards our next-door neighbor. Imagine the uncertainty we have about the distances of so many other galaxies.
你就能明白为什么天文学家一直在寻找所谓的标准烛光——即亮度已知的物体。它们使我们能够利用一系列巧妙的方法估算距离，从而建立起可靠的宇宙测量标尺。它们在建立我们所说的宇宙距离阶梯的过程中发挥了至关重要的作用。
You can see why astronomers are always on the hunt for what are called standard candles—objects with known luminosities. They allow us to estimate distances using a range of ingenious ways of establishing reliable tape measures to the cosmos. And they have been vital in establishing what we call the cosmic distance ladder.
我们利用视差来测量距离，这是测量距离的第一步。得益于依巴谷卫星极其精确的视差测量，我们可以用这种方法非常精确地测量数千光年以内的天体距离。接下来，我们利用造父变星，它使我们能够很好地估算出一亿光年以内的天体距离。至于更高阶的测量，天文学家则使用一些非常复杂且精密的观测方法，这些方法过于专业，此处不赘述，其中许多方法都依赖于标准烛光。
We use parallax to measure distances on the first rung on that ladder. Thanks to Hipparcos’s fantastically accurate parallax measurements, we can measure the distances of objects up to several thousand light-years with great precision this way. We take the next step with Cepheids, which allow us to obtain good estimates of the distances of objects up to a hundred million light-years away. For the next rungs astronomers use a number of exotic and complicated methods too technical to go into here, many of which depend on standard candles.
我们想要测量的距离越远，测量就越发困难。这部分要归功于埃德温·哈勃在1925年做出的惊人发现：宇宙中所有星系都在彼此远离。哈勃的这一发现，是天文学乃至上个世纪整个科学领域最令人震惊和意义最重大的发现之一，其重要性或许只有达尔文通过自然选择发现进化论才能与之媲美。
The distance measurements become more and more tricky the farther out we want to measure. This is partly due to the remarkable discovery in 1925 by Edwin Hubble that all galaxies in the universe are moving away from one another. Hubble’s discovery, one of the most shocking and significant in all of astronomy, perhaps in all of science in the past century, may only be rivaled by Darwin’s discovery of evolution through natural selection.
哈勃观测到，星系发出的光明显向光谱中能量较低的一端（即波长较长的“红色”端）移动。这种现象被称为红移。红移越大，星系远离我们的速度就越快。我们在地球上也用声音的多普勒效应了解这种现象；它解释了为什么我们能够分辨救护车是朝我们驶来还是远离我们，因为……当它高速远离我们时，波数较低；当它高速靠近我们时，波数较高。（我将在第13章更详细地讨论多普勒效应。）
Hubble saw that the light emitted by galaxies showed a distinct shift toward the less energetic end of the spectrum, the “red” end where wavelengths are longer. This is called redshift. The larger the redshift, the faster a galaxy is moving away from us. We know this effect on Earth with sound as the Doppler effect; it explains why we can tell whether an ambulance is coming toward us or going away from us, since the notes are lower when it’s speeding away and higher as it speeds toward us. (I will discuss the Doppler shift in more detail in chapter 13.)
哈勃发现，对于所有他能够测量红移和距离的星系，这些天体距离越远，它们远离我们的速度就越快。因此，宇宙正在膨胀。多么惊人的发现！宇宙中的每一个星系都在加速远离其他每一个星系。
For all the galaxies whose redshifts and distance he could measure, Hubble found that the farther away these objects were, the faster they were moving away. So the universe was expanding. What a monumental discovery! Every galaxy in the universe speeding away from every other galaxy.
当星系距离我们数十亿光年时，这可能会造成距离概念上的极大混淆。我们指的是光线发出时的距离（例如130亿年前），还是指我们认为它现在的距离？毕竟，在过去的130亿年里，该天体与我们的距离已经显著增加。一位天文学家可能会报告说，该天体的距离约为130亿光年（这被称为光时距离），而另一位天文学家可能会报告说，同一天体的距离为290亿光年（这被称为同移距离）。
This can cause great confusion in the meaning of distance when galaxies are billions of light-years away. Do we mean the distance when the light was emitted (13 billion years ago, for instance) or do we mean the distance we think it is now, since the object has substantially increased its distance from us in those 13 billion years? One astronomer may report that the distance is about 13 billion light-years (this is called the light travel time distance) whereas another may report 29 billion light-years for the same object (this is called the co-moving distance).
哈勃的发现后来被称为哈勃定律：星系远离我们的速度与它们与我们的距离成正比。星系距离我们越远，远离的速度就越快。
Hubble’s findings have since become known as Hubble’s law: the velocity at which galaxies move away from us is directly proportional to their distance from us. The farther away a galaxy is, the faster it is racing away.
测量星系的速度相对容易；红移量可以直接转化为星系的速度。然而，要获得精确的距离则截然不同，这才是最难的部分。要知道，哈勃对仙女座星云距离的测量误差高达2.5倍。他提出了一个相当简单的公式：v = H₀D，其中v代表给定星系的速度，D代表该星系到我们的距离， H₀是一个常数，现在被称为哈勃常数。哈勃估计这个常数约为500，单位为千米每秒每百万秒差距（1百万秒差距等于326万光年）。他的常数误差约为10%。例如，根据哈勃的说法，如果一个星系距离我们 5 兆秒差距，那么它相对于我们的速度约为每秒 2500 公里（约每秒 1600 英里）。
Measuring the velocities of the galaxies was relatively easy; the amount of redshift immediately translates into the speed of the galaxy. However, to get accurate distances was a different matter. That was the hardest part. Remember, Hubble’s distance to the Andromeda Nebula was off by a factor of 2.5. He came up with the fairly simple equation v = H0D, where v is the velocity of a given galaxy, D is the distance of that galaxy from us, and H0 is a constant, now called Hubble’s constant. Hubble estimated the constant to be about 500, measured in units of kilometers per second per megaparsec (1 megaparsec is 3.26 million light-years). The uncertainty in his constant was about 10 percent. Thus, as an example, according to Hubble, if a galaxy is at a distance of 5 megaparsecs, its speed relative to us is about 2,500 kilometers per second (about 1,600 miles per second).
宇宙显然正在快速膨胀。但这并非哈勃发现的全部意义。如果你真的知道哈勃常数的值，那么你就可以把时间倒流，从而计算出自那时以来的时间。宇宙大爆炸，以及由此得出的宇宙年龄。哈勃本人估计宇宙的年龄约为20亿年。这一计算结果与地球的年龄相矛盾，地质学家当时测得地球的年龄超过30亿年。这令哈勃非常困扰，原因显而易见。当然，他当时并没有意识到自己犯下了许多系统性错误。他不仅在某些情况下混淆了不同类型的造父变星，而且还将恒星正在形成的气体云误认为是遥远星系中的明亮恒星。
Clearly the universe is expanding fast. But that wasn’t all Hubble’s discovery revealed. If you really knew the value of Hubble’s constant, then you could turn the clock backward in order to calculate the time since the big bang, and thus the age of the universe. Hubble himself estimated that the universe was about 2 billion years old. This calculation was in conflict with the age of the Earth, which geologists were just measuring to be upward of 3 billion years. This bothered Hubble mightily, for good reason. Of course, he was unaware of a number of systematic errors he was making. Not only was he confusing different kinds of Cepheid variables in some cases, but he also mistook clouds of gas in which stars were forming for bright stars in faraway galaxies.
了解过去八十年恒星距离测量进展的一种方法是回顾哈勃常数本身的历史。近一个世纪以来，天文学家一直在努力确定哈勃常数的具体数值，这不仅导致哈勃常数缩小了七倍，从而极大地增加了宇宙的体积，也改变了宇宙的年龄，从哈勃最初估计的20亿年变为我们目前估计的近140亿年——实际上是137.5±1.1亿年。现在，最终，基于部分来自以哈勃命名的卓越轨道望远镜的观测数据，我们达成共识，哈勃常数为每秒每百万秒差距70.4±1.4公里。不确定度仅为2%——这简直令人难以置信！
One way of looking at eighty years’ worth of progress in measuring stellar distances is to look at the history of Hubble’s constant itself. Astronomers have been struggling to nail down the value of Hubble’s constant for nearly a century, which has produced not only a seven-fold reduction in the constant, which dramatically increased the size of the universe, but also changed the age of the universe, from Hubble’s original 2 billion years to our current estimate of nearly 14 billion years—actually 13.75 ± 0.11 billion years. Now, finally, based on observations in part from the fabulous orbiting telescope bearing Hubble’s name, we have a consensus that Hubble’s constant is 70.4 ± 1.4 kilometers per second per megaparsec. The uncertainty is only 2 percent—which is incredible!
想想看，始于 1838 年的视差测量，为开发仪器和数学工具奠定了基础，使我们得以到达数十亿光年外的可观测宇宙边缘。
Just think about it. Parallax measurements, starting in 1838, became the foundation for developing the instruments and mathematical tools to reach billions of light-years to the edge of the observable universe.
尽管我们在解开此类谜团方面取得了显著进展，但当然仍有许多谜团尚未解开。我们可以测量宇宙中暗物质和暗能量的比例，但我们仍然不知道它们究竟是什么。我们知道宇宙的年龄，但仍然好奇它何时、是否会终结，以及将如何终结。我们可以非常精确地测量引力、电磁力以及弱核力和强核力，但我们不知道它们是否最终会被整合到一个统一的理论中。我们也不知道在我们所在的星系或其他星系中存在其他智慧生命的可能性有多大。因此，我们还有很长的路要走。但令人惊叹的是，物理学的工具已经提供了如此多的答案，而且精度如此之高。
For all of our remarkable progress in solving mysteries such as this, there are of course a great many mysteries that remain. We can measure the proportion of dark matter and dark energy in the universe, but we have no idea what they are. We know the age of the universe but still wonder when or if and how it will end. We can make very precise measurements of gravitational attraction, electromagnetism, and of the weak and the strong nuclear forces, but we have no clue if they will ever be combined into one unified theory. Nor do we have any idea what the chances are of other intelligent life existing in our own or some other galaxy. So we have a long way to go. But the wonder is just how many answers the tools of physics have provided, to such a remarkably high degree of accuracy.
第三章
CHAPTER 3
运动中的物体
Bodies in Motion
这里有个有趣的小实验。站在普通的体重秤上——不是医生办公室里那种高级的，也不是那种需要用脚趾敲击才能启动的电子秤，就是普通的体重秤。穿不穿鞋都无所谓（不用刻意表现），看到的数字是多少也无所谓，喜不喜欢也无所谓。现在，迅速踮起脚尖，然后停下来保持这个姿势。你会发现体重秤上的数字会突然剧烈波动。你可能需要重复几次才能看清楚发生了什么，因为整个过程发生得很快。
Here’s something fun to try. Stand on a bathroom scale—not one of those fancy ones at your doctor’s office, and not one of those digital glass things you have to tap with your toes to make it turn on, just an everyday bathroom scale. It doesn’t matter if you have your shoes on (you don’t have to impress anyone), and it doesn’t matter what number you see, and whether you like it or not. Now, quickly raise yourself up on your toes; then stop and hold yourself there. You’ll see that the scale goes a little crazy. You may have to do this several times to clearly see what’s going on because it all happens pretty quickly.
首先，指针会上升，对吧？然后它会大幅下降，最后回到你移动之前的体重位置。不过，根据你使用的体重秤，指针（或数字盘）在稳定下来之前可能还会轻微晃动。接着，当你放下脚后跟时，尤其是如果你动作很快，指针会先下降，然后迅速上升超过你的体重，最后才停在你可能想知道也可能不想知道的体重位置。这到底是怎么回事？毕竟，无论你是脚后跟下沉还是脚尖抬起，你的体重都一样，对吧？真的是这样吗？
First the needle goes up, right? Then it goes way down before it comes back to your weight, where it was before you moved, though depending on your scale, the needle (or numbered disk) might still jiggle a bit before it stabilizes. Then, as you bring your heels down, especially if you do so quickly, the needle first goes down, then shoots up past your weight, before coming to rest back at the weight you may or may not have wanted to know. What was that all about? After all, you weigh the same whether you move your heels down or up on your toes, right? Or do you?
要弄清这个问题，我们需要——信不信由你——艾萨克·牛顿爵士，他是我心目中史上最伟大的物理学家。我的一些同事对此持不同意见，当然你也可以为阿尔伯特·爱因斯坦辩护，但没有人真正质疑爱因斯坦和牛顿是否是顶尖的两位。我为什么选择牛顿？因为他的发现既基础又广泛。他研究了光的本质，并发展了色彩理论。为了研究行星运动，他建造了第一架反射望远镜，这比当时的折射望远镜有了重大进步，即使在今天，几乎所有的大型望远镜都遵循着他设计的基本原理。在研究流体运动特性方面，他开创了物理学的一个重要领域，并且成功计算出了声速（误差只有大约15%）。牛顿甚至发明了一个全新的数学分支：微积分。幸运的是，我们不需要借助微积分就能理解他最杰出的成就，这些成就后来被称为牛顿定律。我希望在本章中，我能向你们展示这些看似简单的定律实际上有多么深远。
To figure this out, we need, believe it or not, Sir Isaac Newton, my candidate for the greatest physicist of all time. Some of my colleagues disagree, and you can certainly make a case for Albert Einstein, but no one really questions whether Einstein and Newton are the top two. Why do I vote for Newton? Because his discoveries were both so fundamental and so diverse. He studied the nature of light and developed a theory of color. To study the planetary motions he built the first reflecting telescope, which was a major advance over the refracting telescopes of his day, and even today almost all the major telescopes follow the basic principles of his design. In studying the properties of the motion of fluids, he pioneered a major area of physics, and he managed to calculate the speed of sound (he was only off by about 15 percent). Newton even invented a whole new branch of mathematics: calculus. Fortunately, we don’t need to resort to calculus to appreciate his most masterful achievements, which have come to be known as Newton’s laws. I hope that in this chapter I can show you how far-reaching these apparently simple laws really are.
牛顿三大运动定律
Newton’s Three Laws of Motion
第一定律指出，静止的物体将保持静止状态，运动的物体将保持匀速直线运动状态——除非受到外力作用。或者用牛顿自己的话说，“物体将保持静止状态或匀速直线运动状态，除非受到外力作用而改变这种状态。” 这就是惯性定律。
The first law holds that a body at rest will persist in its state of being at rest, and a body in motion will persist in its motion in the same direction with the same speed—unless, in either case, a force acts on it. Or, in Newton’s own words, “A body at rest perseveres in its state of rest, or of uniform motion in a right line unless it is compelled to change that state by forces impressed upon it.” This is the law of inertia.
惯性的概念我们并不陌生，但仔细想想，你就会发现它其实有多么违反直觉。我们现在习以为常地接受这条定律，尽管它显然与我们的日常经验相悖。毕竟，运动的物体很少会沿着直线运动，而且它们通常也不会无限运动下去。我们预期它们最终会停下来。高尔夫球手不可能提出惯性定律，因为很少有推杆是直线运动的，而且很多推杆都会停在球的末端。距离洞口还差一点。过去和现在人们都凭直觉认为，事物自然趋向静止——这正是为什么在牛顿取得突破之前，这种观点主导了西方数千年来对这些问题的看法。
The concept of inertia is familiar to us, but if you reflect on it for a bit, you can appreciate how counterintuitive it actually is. We take this law for granted now, even though it runs clearly against our daily experience. After all, things that move rarely do so along a straight line. And they certainly don’t usually keep moving indefinitely. We expect them to come to a stop at some point. No golfer could have come up with the law of inertia, since so few putts go in a straight line and so many stop well short of the hole. What was and still is intuitive is the contrary idea—that things naturally tend toward rest—which is why it had dominated Western thinking about these matters for thousands of years until Newton’s breakthrough.
牛顿彻底颠覆了我们对物体运动的理解，他解释说，高尔夫球经常在进洞前停住的原因是摩擦力使其减速，而月球不会飞向太空而是继续绕地球旋转的原因是引力将其保持在轨道上。
Newton turned our understanding of the motion of objects on its head, explaining that the reason a golf ball often stops short of the hole is that the force of friction is slowing it down, and the reason the Moon doesn’t shoot off into space, but keeps circling Earth, is that the force of gravitational attraction is holding it in orbit.
为了更直观地体会惯性，不妨想想在冰上滑行时，在冰场尽头转弯有多么困难——你的身体会不由自主地想要保持直线滑行，你必须掌握好力度，以合适的角度控制冰鞋，才能顺利地离开冰面，避免胡乱挥舞或撞到墙壁。或者，如果你是一名滑雪者，想想快速改变路线以避开疾驰而来的滑雪者有多么困难。之所以在这些情况下我们比平时更能感受到惯性，是因为在这两种情况下，几乎没有摩擦力来减缓我们的速度并帮助我们改变运动状态。试想一下，如果高尔夫球场的果岭是由冰制成的，你就会深刻地体会到高尔夫球有多么渴望一直滑下去。
To appreciate the reality of inertia more intuitively, think about how difficult it can be when you are ice skating to make the turn at the end of the rink—your body wants to keep going straight and you have to learn just how much force to apply to your skates at just the right angle to move yourself off of that course without flailing wildly or crashing into the wall. Or if you are a skier, think of how difficult it can be to change course quickly to avoid another skier hurtling into your path. The reason we notice inertia so much more in these cases than we generally do is that in both cases there is so little friction acting to slow us down and help us change our motion. Just imagine if putting greens were made of ice; then you would become acutely aware of just how much the golf ball wants to keep going and going.
想想这是多么革命性的发现。它不仅颠覆了以往所有的认知，还为我们揭示了许多无形却时刻作用于我们身上的力——例如摩擦力、引力、磁力和电力。他的贡献如此重要，以至于物理学中力的单位被命名为牛顿。牛顿不仅让我们“看到”了这些隐藏的力，还向我们展示了如何测量它们。
Consider just how revolutionary an insight this was. Not only did it overturn all previous understanding; it pointed the way to the discovery of a host of forces that are acting on us all the time but are invisible—like friction, gravity, and the magnetic and electric forces. So important was his contribution that in physics the unit of force is called a newton. But not only did Newton allow us to “see” these hidden forces; he also showed us how to measure them.
他提出的第二定律为计算力提供了一种极其简单却又强大的方法。第二定律被一些人认为是物理学中最重要的方程式，它就是著名的F = ma。简单来说：物体所受的合力F等于物体的质量m乘以物体的合加速度a 。
With the second law he provided a remarkably simple but powerful guide for calculating forces. Considered by some the most important equation in all of physics, the second law is the famous F = ma. In words: the net force, F, on an object is the mass of the object, m, multiplied by the net acceleration, a, of the object.
为了了解这个公式在日常生活中的用途，不妨以X光机为例。如何产生合适能量范围的X射线至关重要。以下是牛顿方程如何帮助我们做到这一点。
To see just one way in which this formula is so useful in our daily lives, take the case of an X-ray machine. Figuring out how to produce just the right range of energies for the X-rays is crucial. Here’s how Newton’s equation lets us do just that.
物理学的一项重要发现（我们稍后会详细探讨）是，带电粒子（例如电子、质子或离子）在电场中会受到力的作用。如果我们知道粒子的电荷量和电场强度，就可以计算出作用在该粒子上的电场力。然而，一旦我们知道了电场力的大小，就可以利用牛顿第二定律计算出粒子的加速度。*
One of the major findings in physics—which we’ll explore more later—is that a charged particle (say an electron or proton or ion) will experience a force when it is placed in an electric field. If we know the charge of the particle and the strength of the electric field, we can calculate the electric force acting on that particle. However, once we do know the force, using Newton’s second law we can calculate the acceleration of the particle.*
在X射线机中，电子在撞击X射线管内的靶材之前会被加速。电子撞击靶材的速度决定了随后产生的X射线的能量范围。通过改变电场强度，我们可以改变电子的加速度。因此，可以通过控制电子撞击靶材的速度来选择所需的X射线能量范围。
In an X-ray machine electrons are accelerated before they strike a target inside the X-ray tube. The speed with which the electrons hit the target determines the energy range of the X-rays that are then produced. By changing the strength of the electric field, we can change the acceleration of the electrons. Thus the speed with which the electrons hit the target can be controlled to select the desired energy range of the X-rays.
为了便于进行此类计算，物理学家使用牛顿作为力的单位——1牛顿是指使1千克质量的物体产生1米/秒²加速度的力。为什么我们说“每秒每秒”呢？因为加速度的作用下，速度是不断变化的；换句话说，它不会在第一秒之后就停止。如果加速度是恒定的，那么速度每秒变化的量是相同的。
In order to facilitate making such calculations, physicists use as a unit of force, the newton—1 newton is the force that accelerates a mass of 1 kilogram at 1 meter per second per second. Why do we say “per second per second”? Because with acceleration, the velocity is constantly changing; so, in other words, it doesn’t stop after the first second. If the acceleration is constant, the velocity is changing by the same amount every second.
为了更清楚地理解这一点，不妨以一个从曼哈顿高楼（为什么不是帝国大厦的观景台？）上扔下的保龄球为例。众所周知，物体在地球上自由落体的加速度约为9.8米/秒²；这被称为重力加速度，在物理学中用g表示。（对于为了简化计算（我暂时忽略空气阻力；稍后会详细讨论）。保龄球在第一秒后的速度为每秒 9.8 米。到第二秒结束时，它的速度将再增加每秒 9.8 米，达到每秒 19.6 米。到第三秒结束时，它的速度将达到每秒 29.4 米。保龄球大约需要 8 秒才能落地。落地后，它的速度约为 9.8 的 8 倍，即每秒约 78 米（约 175 英里/小时）。
To see this more clearly, take the case of a bowling ball dropped from a tall building in Manhattan—why not from the observation deck of the Empire State Building? It is known that the acceleration of objects dropped on Earth is approximately 9.8 meters per second per second; it is called the gravitational acceleration, represented in physics by g. (For simplicity I am ignoring air drag for now; more about this later.) After the first second the bowling ball has a speed of 9.8 meters per second. By the end of the second second, it will pick up an additional 9.8 meters per second of speed, so it will be moving at 19.6 meters per second. And by the end of the third second it will be traveling 29.4 meters per second. It takes about 8 seconds for the ball to hit the ground. Its speed is then about 8 times 9.8, which is about 78 meters per second (about 175 miles per hour).
那么，关于从帝国大厦顶楼扔下一枚硬币会砸死人的说法又该如何解释呢？我再次先忽略空气阻力的影响，我强调在这种情况下空气阻力会相当大。但即使不考虑空气阻力，一枚以大约每小时175英里的速度砸到你身上，大概也不会致命。
What about the much repeated notion that if you threw a penny off the top of the Empire State Building it would kill someone? I’ll again exclude the role of air drag, which I emphasize would be considerable in this case. But even without that factored in, a penny hitting you with a speed of about 175 miles per hour will probably not kill you.
这里正好可以探讨本书中反复出现的一个问题，主要是因为它在物理学中也反复出现：质量和重量的区别。请注意，牛顿在他的公式中使用的是质量而不是重量，虽然你可能认为两者相同，但它们本质上是不同的。我们通常使用磅和千克（本书中也将使用的单位）作为重量单位，但实际上它们是质量单位。
This is a good place to grapple with an issue that will come up over and over in this book, mainly because it comes up over and over in physics: the difference between mass and weight. Note that Newton used mass in his equation rather than weight, and though you might think of the two as being the same, they’re actually fundamentally different. We commonly use the pound and the kilogram (the units we’ll use in this book) as units of weight, but the truth is that they are units of mass.
区别其实很简单。无论你在宇宙的哪个角落，你的质量都是一样的。没错——无论是在月球上、外太空，还是小行星表面。真正变化的是你的重量。那么，重量究竟是什么呢？这就有点复杂了。重量是引力作用的结果。重量是一种力：它等于质量乘以重力加速度（F = mg）。因此，我们的重量会随着作用在我们身上的引力强度而变化，这就是为什么宇航员在月球上的重量会减轻。月球的引力大约是地球的六分之一，所以宇航员在月球上的重量大约是他们在地球上的六分之一。
The difference is actually simple. Your mass is the same no matter where you are in the universe. That’s right—on the Moon, in outer space, or on the surface of an asteroid. It’s your weight that varies. So what is weight, then? Here’s where things get a little tricky. Weight is the result of gravitational attraction. Weight is a force: it is mass times the gravitational acceleration (F = mg). So our weight varies depending upon the strength of gravity acting on us, which is why astronauts weigh less on the Moon. The Moon’s gravity is about a sixth as strong as Earth’s, so on the Moon astronauts weigh about one-sixth what they weigh on Earth.
对于给定的质量，地球的引力在地球上任何地方都大致相同。所以我们可以说，“她体重120磅” *或“他重80公斤”，*即使这样做会混淆质量和重量这两个概念。我反复思考是否要在本书中使用物理上表示力（也就是重量）的单位，而不是千克和磅，最终还是放弃了，因为那样会造成混淆——没有人，即使是质量为 80 千克的物理学家，也不会说“我的体重是 784 牛顿”（80 × 9.8 = 784）。所以，我希望你们记住这个区别——我们稍后会再讨论这个问题，届时我们将回到为什么当我们踮起脚尖站在秤上时，秤会失灵。
For a given mass, the gravitational attraction of the Earth is about the same no matter where you are on it. So we can get away with saying, “She weighs a hundred twenty pounds”* or “He weighs eighty kilograms,”* even though by doing so we are confusing these two categories (mass and weight). I thought long and hard about whether to use the technical physics unit for force (thus weight) in this book instead of kilos and pounds, and decided against it on the grounds that it would be too confusing—no one, not even a physicist whose mass is 80 kilograms would say, “I weigh seven hundred eighty-four newtons” (80 × 9.8 = 784). So instead I’ll ask you to remember the distinction—and we’ll come back to it in just a little while, when we return to the mystery of why a scale goes crazy when we stand on our tiptoes on it.
地球上各处的引力加速度几乎相同，这一事实背后隐藏着一个你可能听说过的谜团：不同质量的物体下落速度相同。关于伽利略的一个著名故事，最早出现在早期的一部传记中，讲述了他站在比萨斜塔顶端，同时从塔上扔下一个炮弹和一个较小的木球。据说，他的目的是为了反驳亚里士多德提出的“重物比轻物下落速度更快”的论断。这个故事早已受到质疑，现在看来，伽利略从未进行过这项实验，但这仍然是一个引人入胜的故事——如此精彩的故事，以至于阿波罗15号登月任务的指挥官大卫·斯科特也曾做过一个著名的实验：同时将一把锤子和一根猎鹰羽毛扔到月球表面，以观察不同质量的物体在真空中是否会以相同的速度下落。这是一个很棒的视频，您可以在这里观看：http://video.google.com/videoplay?docid= 6926891572259784994 # 。
The fact that gravitational acceleration is effectively the same everywhere on Earth is behind a mystery that you may well have heard of: that objects of different masses fall at the same speed. A famous story about Galileo, which was first told in an early biography, recounts that he performed an experiment from the top of the Leaning Tower of Pisa in which he threw a cannonball and a smaller wooden ball off the tower at the same time. His intent, reputedly, was to disprove an assertion attributed to Aristotle that heavier objects would fall faster than light ones. The account has long been doubted, and it seems pretty clear now that Galileo never did perform this experiment, but it still makes for a good story—such a good story that the commander of the Apollo 15 Moon mission, David Scott, famously dropped a hammer and a falcon feather onto the surface of the Moon at the same time to see if objects of different mass would fall to the ground at the same rate in a vacuum. It’s a wonderful video, which you can access here: http://video.google.com/videoplay?docid=6926891572259784994#.
这段视频最让我惊讶的是，它们下落的速度都非常慢。乍一看，你可能会觉得它们都会很快下落，至少锤子肯定会很快。但它们下落得很慢，因为月球上的重力加速度大约只有地球的六分之一。
The striking thing to me about this video is just how slowly they both drop. Without thinking about it, you might expect them both to drop quickly, at least surely the hammer. But they both fall slowly because the gravitational acceleration on the Moon is about six times less than it is on Earth.
为什么伽利略关于两个质量不同的物体会同时落地的预言是正确的？原因在于所有物体受到的万有引力加速度相同。根据万有引力定律F = ma，质量越大，引力越大，但加速度对所有物体而言是相同的。因此，它们以相同的速度落地。当然，质量较大的物体拥有更多的能量，因此落地时的冲击力也更大。
Why was Galileo right that two objects of different mass would land at the same time? The reason is that the gravitational acceleration is the same for all objects. According to F = ma, the larger the mass, the larger the gravitational force, but the acceleration is the same for all objects. Thus they reach the ground with the same speed. Of course, the object with the larger mass will have more energy and will therefore have a greater impact.
需要注意的是，如果在地球上进行这个实验，羽毛和锤子不会同时落地。这是空气阻力造成的，我们之前一直忽略了它。空气阻力是一种阻碍物体运动的力。此外，风对羽毛的影响远大于对锤子的影响。
Now it’s important to note here that the feather and the hammer would not land at the same time if you performed this experiment on Earth. This is the result of air drag, which we’ve discounted until now. Air drag is a force that opposes the motion of moving objects. Also wind would have much more effect on the feather than on the hammer.
这就引出了牛顿第二定律的一个非常重要的特征。上述等式中的“合力”一词至关重要，因为在自然界中，几乎总是有多个力作用于物体；所有这些力都必须考虑在内。这意味着必须将这些力相加。然而，实际情况并非如此简单，因为力是矢量，这意味着它们既有大小又有方向，所以你不能像 2 + 3 = 5 那样简单地计算合力。假设只有两个力作用于一个 4 千克的物体上：一个 3 牛顿的力向上，另一个 2 牛顿的力向下。这两个力的合力为 1 牛顿，方向向上。根据牛顿第二定律，物体将以 0.25 米/秒² 的加速度向上运动。
This brings us to a very important feature of the second law. The word net in the equation as given above is vital, as nearly always in nature more than one force is acting on an object; all have to be taken into account. This means that the forces have to be added. Now, it’s not really as simple as this, because forces are what we call vectors, meaning that they have a magnitude as well as a direction, which means that you cannot really make a calculation like 2 + 3 = 5 for determining the net force. Suppose only two forces act on a mass of 4 kilograms; one force of 3 newtons is pointing upward, and another of 2 newtons is pointing downward. The sum of these two forces is then 1 newton in the upward direction and, according to Newton’s second law, the object will be accelerated upward with an acceleration of 0.25 meters per second per second.
两个力的合力甚至可以为零。如果我把一个质量为m的物体放在桌子上，根据牛顿第二定律，物体受到的重力为mg（质量 × 重力加速度）牛顿，方向向下。由于物体没有加速度，因此物体受到的合力必须为零。这意味着必然存在另一个大小为mg牛顿的向上力。这就是桌子向上推物体的力。向下的mg力和向上的mg力之和为零！
The sum of two forces can even be zero. If I place an object of mass m on my table, according to Newton’s second law, the gravitational force on the object is then mg (mass × gravitational acceleration) newtons in the downward direction. Since the object is not being accelerated, the net force on the object must be zero. That means that there must be another force of mg newtons upward. That is the force with which the table pushes upward on the object. A force of mg down and one of mg up add up to a force of zero!
这就引出了牛顿第三定律：“每一个作用力都必然有其作用力。”“作用力与反作用力大小相等，方向相反。” 这意味着两个物体相互作用的力总是大小相等、方向相反的。我喜欢这样说：作用力等于反作用力的负值，或者更通俗地说，“每一个作用力都有一个大小相等、方向相反的反作用力。”
This brings us to Newton’s third law: “To every action there is always an equal and opposite reaction.” This means that the force that two objects exert on each other are always equal and are directed in opposite directions. As I like to put it, action equals minus reaction, or, as it’s known more popularly, “For every action there is an equal and opposite reaction.”
这条定律的一些推论很容易理解：步枪开火时会向后顶住你的肩膀。但想想看，当你推墙时，墙也会以大小相等的力反作用于你。你生日吃的草莓蛋糕压在蛋糕盘上，蛋糕盘也以大小相等的力反作用于蛋糕盘。事实上，尽管第三定律听起来有些奇怪，但我们身边到处都是它发挥作用的例子。
Some of the implications of this law are intuitive: a rifle recoils backward against your shoulder when it fires. But consider also that when you push against a wall, it pushes back on you in the opposite direction with the exact same force. The strawberry shortcake you had for your birthday pushed down on the cake plate, which pushed right back at it with an equal amount of force. In fact, odd as the third law is, we are completely surrounded by examples of it in action.
你有没有打开过连接着地上水管的水龙头，然后看到水管像蛇一样四处乱窜，运气好的话还能喷到你弟弟？这是为什么呢？因为水从水管里喷出来的时候，也会反过来推动水管，结果就是水管像鞭子一样四处摆动。或者你肯定也吹过气球，然后松手让它在房间里乱飞。这是因为气球向外喷射空气，而从气球里喷出的空气反过来又推动气球，使它像蛇一样四处乱窜，就像空中版的蛇形水管。这和喷气式飞机和火箭的原理是一样的。它们高速喷射气体，从而产生反作用力。
Have you ever turned on the faucet connected to a hose lying on the ground and seen the hose snake all over the place, maybe spraying your little brother if you were lucky? Why does that happen? Because as the water is pushed out of the hose, it also pushes back on the hose, and the result is that the hose is whipped all around. Or surely you’ve blown up a balloon and then let go of it to see it fly crazily around the room. What’s happening is that the balloon is pushing the air out, and the air coming out of the balloon pushes back on the balloon, making it zip around, an airborne version of the snaking garden hose. This is no different from the principle behind jet planes and rockets. They eject gas at a very high speed and that makes them move in the opposite direction.
为了真正理解这个洞见有多么奇特和深刻，不妨想想，如果我们从三十层楼顶扔下一个苹果，牛顿定律会告诉我们什么。我们知道加速度是g，大约是 9.8 米每秒平方英寸。假设苹果的质量大约是半千克（约 1.1 磅）。根据牛顿第二定律F = ma，我们发现地球对苹果的引力为 0.5 × 9.8 = 4.9 牛顿。到目前为止，一切都说得通。
Now, to truly grasp just how strange and profound an insight this is, consider what Newton’s laws tell us is happening if we throw an apple off the top of a thirty-story building. We know the acceleration will be g, about 9.8 meters per second per second. Now, say the apple is about half a kilogram (about 1.1 pounds) in mass. Using the second law, F = ma, we find that the Earth attracts the apple with a force of 0.5 × 9.8 = 4.9 newtons. So far so good.
但现在考虑一下第三定律的要求：如果地球以 4.9 牛顿的力吸引苹果，那么苹果也会吸引地球。地球以 4.9 牛顿的力作用于苹果。因此，当苹果落向地球时，地球也向苹果落下。这听起来很荒谬，对吧？但别急。由于地球的质量远大于苹果，计算结果会变得非常复杂。我们知道地球的质量约为 6 × 10²⁴千克，因此可以计算出它向苹果下落的距离：大约 10⁻²²米，约为质子大小的千万分之一，这个距离小到无法测量；事实上，它毫无意义。
But now consider what the third law demands: if the Earth attracts the apple with a force of 4.9 newtons, then the apple will attract the Earth with a force of 4.9 newtons. Thus, as the apple falls to Earth, the Earth falls to the apple. This seems ridiculous, right? But hold on. Since the mass of the Earth is so much greater than that of the apple, the numbers get pretty wild. Since we know that the mass of the Earth is about 6 × 1024 kilograms, we can calculate how far it falls up toward the apple: about 10–22 meters, about one ten-millionth of the size of a proton, a distance so small it cannot even be measured; in fact, it’s meaningless.
这种两个物体之间作用力大小相等、方向相反的原理，在我们生活中无处不在，也是为什么当你踮起脚尖站在体重秤上时，秤上的数字会剧烈波动的原因。这让我们回到“重量究竟是什么”这个问题，并让我们更精确地理解它。
This whole idea, that the force between two bodies is both equal and in opposite directions, is at play everywhere in our lives, and it’s the key to why your scale goes berserk when you lift yourself up onto your toes on it. This brings us back to the issue of just what weight is, and lets us understand it more precisely.
当你站在体重秤上时，重力以mg的力向下作用于你（其中m是你的质量），而体重秤则以相同的力向上作用于你，因此你受到的合力为零。体重秤实际测量的是这个向上作用于你的力，也就是我们所说的你的体重。记住，体重和质量并不相同。要改变你的质量，你需要节食（当然，你也可以反其道而行之，吃得更多），但你的体重更容易改变。
When you stand on a bathroom scale, gravity is pulling down on you with force mg (where m is your mass) and the scale is pushing up on you with the same force so that the net force on you is zero. This force pushing up against you is what the scale actually measures, and this is what registers as your weight. Remember, weight is not the same thing as mass. For your mass to change, you’d have to go on a diet (or, of course, you might do the opposite, and eat more), but your weight can change much more readily.
假设你的质量 ( m ) 为 55 千克（约 120 磅）。当你站在浴室的体重秤上时，你向下按压体重秤，施加一个力mg ，体重秤也会以同样的力mg反作用于你。你受到的合力为零。体重秤反作用于你的力就是你在体重秤上读到的数值。由于你的体重秤可能以磅为单位显示体重，因此它会显示 120 磅。
Let’s say that your mass (m) is 55 kilograms (that’s about 120 pounds). When you stand on a scale in your bathroom, you push down on the scale with a force mg, and the scale will push back on you with the same force, mg. The net force on you is zero. The force with which the scale pushes back on you is what you will read on the scale. Since your scale may indicate your weight in pounds, it will read 120 pounds.
现在我们来在电梯里给你称一下体重。当电梯静止不动（或者以恒定速度运行）时，你（以及电梯）都没有加速，体重秤会显示你的体重是120磅，就像你在浴室里称重时一样。我们进入电梯（电梯处于静止状态），你站上体重秤，读数是120磅。现在我按下顶楼按钮，然后……电梯短暂加速向上以达到所需速度。假设这个加速度是 2 米/秒²，并且是恒定的。在电梯加速的短暂时间内，你受到的合力不可能为零。根据牛顿第二定律，你受到的合力F <sub>net </sub>必须等于ma<sub> net</sub>。由于合加速度是 2 米/秒²，你受到的合力是m × 2 向上。由于你受到的重力是mg向下，所以你还受到一个mg + m²的向上力，也可以写成m ( g + 2)。这个力从哪里来呢？它肯定来自体重秤（还能来自哪里呢？）。体重秤对你施加了一个m ( g + 2) 的向上力。但请记住，体重秤显示的重量是它对你施加的向上力。因此，体重秤告诉你你的体重约为 144 磅（记住，g约为 10 米/秒²）。你体重增加了不少！
Let’s now weigh you in an elevator. While the elevator stands still (or while the elevator is moving at constant speed), you are not being accelerated (neither is the elevator) and the scale will indicate that you weigh 120 pounds, as was the case when you weighed yourself in your bathroom. We enter the elevator (the elevator is at rest), you go on the scale, and it reads 120 pounds. Now I press the button for the top floor, and the elevator briefly accelerates upward to get up to speed. Let’s assume that this acceleration is 2 meters per second per second and that it is constant. During the brief time that the elevator accelerates, the net force on you cannot be zero. According to Newton’s second, the net force Fnet on you must be Fnet = manet. Since the net acceleration is 2 meters per second per second, the net force on you is m × 2 upward. Since the force of gravity on you is mg down, there must be a force of mg + m2, which can also be written as m(g + 2), on you in upward direction. Where does this force come from? It must come from the scale (where else?). The scale is exerting a force m(g + 2) on you upward. But remember that the weight that the scale indicates is the force with which it pushes upward on you. Thus the scale tells you that your weight is about 144 pounds (remember, g is about 10 meters per second per second). You have gained quite a bit of weight!
根据牛顿第三定律，如果秤对你施加一个向上的力m ( g +2)，那么你必须对秤施加同样大小的向下的力。你可能会想，如果秤对你施加的力与你对秤施加的力大小相等，那么你受到的合力为零，因此你不会产生加速度。如果你这样想，就犯了一个非常常见的错误。作用在你身上的力只有两个：重力mg （向下）和秤对你施加的向上的力m ( g +2)。因此，你受到的合力为 2m，方向向上，这将使你产生 2 米/秒² 的加速度。
According to Newton’s third, if the scale exerts a force of m(g + 2) on you upward, then you must exert the same force on the scale downward. You may now reason that if the scale pushes on you with the same force that you push on the scale, that then the net force on you is zero, thus you cannot be accelerated. If you reason this way, you make a very common mistake. There are only two forces acting on you: mg down due to gravity and m(g + 2) up due to the scale, and thus a net force of 2m is exerted on you in an upward direction, which will accelerate you at 2 meters per second per second.
电梯停止加速的那一刻，你的体重就会恢复正常。因此，你的体重只有在电梯向上加速的短暂时间内才会增加。
The moment the elevator stops accelerating, your weight goes back to normal. Thus it’s only during the short time of the upward acceleration that your weight goes up.
现在你应该能自己明白，如果电梯向下加速，你的体重就会减轻。当向下加速度为 2 米/秒² 时，体重秤会显示你的体重为m ( g -2)，约为 96 磅。由于向上运行的电梯最终必须停止，因此在停止之前它必须短暂地向下加速。所以，在电梯即将到达终点时，你的体重会减轻。乘电梯上去后，你会发现自己瘦了，你可能会很高兴！然而，不久之后，当电梯停下来时，你的体重就会恢复正常（120磅）。
You should now be able to figure out on your own that if the elevator is being accelerated downward, you lose weight. During the time that the acceleration downward is 2 meters per second per second, the scale will register that your weight is m(g – 2), which is about 96 pounds. Since an elevator that goes up must come to a halt, it must be briefly accelerated downward before it comes to a stop. Thus near the end of your elevator ride up you will see that you lost weight, which you may enjoy! However, shortly after that, when the elevator has come to a stop, your weight will again go back to normal (120 pounds).
假设现在，一个非常非常讨厌你的人剪断了电梯缆绳，你开始以重力加速度g 沿着电梯井快速下滑。我知道你那时可能不会想到物理，但这会是一次（短暂的）有趣体验。你的体重会变成m ( g - g ) = 0；你处于失重状态。因为秤和你以相同的加速度向下坠落，它不再对你施加向上的力。如果你低头看秤，它会显示零。实际上，你会漂浮在空中，电梯里的所有东西也会漂浮在空中。如果你手里拿着一杯水，你可以把它倒过来，水也不会洒出来，当然，我强烈建议你不要尝试这个实验！
Suppose now, someone who really, really dislikes you cuts the cable and you start zooming down the elevator shaft, going down with an acceleration of g. I realize you probably wouldn’t be thinking about physics at that point, but it would make for a (briefly) interesting experience. Your weight will become m(g – g) = 0; you are weightless. Because the scale is falling downward at the same acceleration as you, it no longer exerts a force on you upward. If you looked down at the scale it would register zero. In truth, you would be floating, and everything in the elevator would be floating. If you had a glass of water you could turn it over and the water would not fall out, though of course this is one experiment I urge you not to try!
这就解释了为什么宇航员在宇宙飞船里会漂浮。当航天器或航天飞机在轨道上运行时，它实际上处于自由落体状态，就像电梯的自由落体一样。那么，自由落体究竟是什么呢？答案或许会让你感到惊讶。自由落体是指作用在你身上的力只有引力，没有其他力作用于你。在轨道上，宇航员、宇宙飞船以及飞船内部的所有物体都在自由落体地向地球坠落。宇航员之所以不会摔得粉碎，是因为地球是曲面的，而且宇航员、飞船以及飞船内部的所有物体运动速度极快，以至于在他们向地球坠落的过程中，地球表面会向外弯曲，从而使他们永远不会撞击地球表面。
This explains why astronauts float in spaceships. When a space module, or the space shuttle, is in orbit, it is actually in a state of free fall, just like the free fall of the elevator. What exactly is free fall? The answer might surprise you. Free fall is when the force acting upon you is exclusively gravitational, and no other forces act on you. In orbit, the astronauts, the spaceship, and everything inside it are all falling toward Earth in free fall. The reason why the astronauts don’t go splat is because the Earth is curved and the astronauts, the spaceship, and everything inside it are moving so fast that as they fall toward Earth, the surface of the planet curves away from them, and they will never hit the Earth’s surface.
因此，航天飞机上的宇航员处于失重状态。如果你身处航天飞机内，你会感觉不到重力；毕竟，航天飞机上的任何东西都没有重量。人们常说，航天飞机在轨道上处于零重力环境，因为这是你的感知。然而，如果没有重力，航天飞机就无法保持在轨道上。
Thus the astronauts in the shuttle are weightless. If you were in the shuttle, you would think that there is no gravity; after all, nothing in the shuttle has any weight. It’s often said that the shuttle in orbit is a zero-gravity environment, since that’s the way you perceive it. However, if there were no gravity, the shuttle would not stay in orbit.
改变体重这个想法太迷人了，我真的很想能够展示这种现象——甚至是失重——同学们，如果我爬上一张桌子，脚上绑着一个体重秤，结果会怎么样？我想，或许我可以架设一台特殊的摄像机，向学生们展示，在我自由落体的那半秒钟左右，体重秤会显示零。我建议你们自己试试，但别费劲了；相信我，我试过很多次，结果只是弄坏了好几个秤。问题在于，市面上卖的体重秤反应速度太慢，因为它们的弹簧有惯性。这真是牛顿定律的悖论！如果你能从三十层楼跳下去，或许有足够的时间（大约4.5秒）观察到这种现象，但当然，这个实验还会存在其他问题。
The whole idea of changing weight is so fascinating that I really wanted to be able to demonstrate this phenomenon—even weightlessness—in class. What if I climbed up on a table, standing on a bathroom scale that was tied very securely to my feet? I thought then maybe I could somehow show my students—by rigging up a special camera—that for the half second or so that I was in free fall the bathroom scale would indicate zero. I might recommend that you try this yourself, but don’t bother; trust me, I tried it many times and only broke many scales. The problem is that the scales you can buy commercially don’t react nearly fast enough, since there is inertia in their springs. One of Newton’s laws bedeviling another! If you could jump off a thirty-story building, you would probably have enough time (you would have about 4.5 seconds) to see the effect, but of course there would be other problems with that experiment.
所以，与其费劲地砸秤或从楼上跳下来，不如试试这个方法，在自家后院体验失重感——前提是你有一张野餐桌，而且膝盖没问题。我是在教室前面的实验台上做的。爬上桌子，伸出双手，轻轻托住一加仑或半加仑的水壶，不要抓住壶身，水壶必须只是轻轻地放在你的手上。然后从桌子上跳下去，在空中你会看到水壶开始漂浮在你的手上方。如果你能让朋友帮你拍下跳下去的视频，然后慢放，你会非常清楚地看到水壶开始漂浮。为什么呢？因为当你向下加速时，你之前用来托住水壶的力就消失了。水壶现在的加速度和你一样，都是9.8米/秒²。你和水壶都在自由落体。
So rather than breaking scales or jumping off buildings, here’s something you can try in your backyard to experience weightlessness, if you have a picnic table and good knees. I do this from the lab table in front of my classroom. Climb up on the table and hold a gallon or half-gallon jug of water in your outstretched hands, just cradling it lightly on top of them, not holding the sides of the jug. It has to be just resting on your hands. Now jump off the table, and while you are in the air you will see the jug start floating above your hands. If you can get a friend to make a digital video of you taking the jump, and play it back in slow motion, you will very clearly see the jug of water start to float. Why? Because as you accelerate downward the force with which you have been pushing up on the jug, to keep it in your hands, has become zero. The jug will now be accelerated at 9.8 meters per second per second, just as you are. You and the jug are both in free fall.
但这一切如何解释当你踮起脚尖时体重秤上的数字会突然飙升呢？当你向上蹬地时，你的身体会加速上升，体重秤对你的压力也会随之增大。因此，在那短暂的瞬间，你的体重会增加。但当你踮起脚尖到达最高点时，速度会减慢直至停止，这意味着你的体重会下降。然后，当你放下脚后跟时，整个过程会反向进行。你刚刚就演示了如何在不改变自身质量的情况下，在极短的时间内改变自己的体重。
But how does all of this explain why your scale goes berserk when you lift yourself up on your toes? As you push yourself upward you accelerate upward, and the force of the scale pushing on you increases. So you weigh more for that brief time. But then, at the top of your toes, you decelerate to come to a halt, and that means that your weight goes down. Then, when you let your heels down, the entire process is reversed, and you have just demonstrated how, without changing your mass at all, you can make yourself weigh more or less for fractions of a second.
万有引力定律：牛顿与苹果
The Law of Universal Gravitation: Newton and the Apple
人们通常提到牛顿三大定律，但实际上他提出了四条定律。我们都听过牛顿在果园里观察苹果从树上掉落的故事。牛顿的一位早期传记作者声称，这个故事是牛顿本人讲述的。“事情的起因是一个苹果的掉落，”牛顿的朋友威廉·斯图克利引用他与牛顿的一次谈话写道，“当时牛顿正沉思着。他心想，为什么苹果总是垂直落到地上呢？”但许多人仍然不相信这个故事的真实性。毕竟，牛顿只是在去世前一年才把这个故事告诉了斯图克利，而且在他浩瀚的著作中，他从未在其他任何地方提及过此事。
People commonly refer to Newton’s three laws, but, in fact, he formulated four. We’ve all heard the story of Newton observing an apple falling from a tree one day in his orchard. One of Newton’s early biographers claimed that Newton himself told the story. “It was occasion’d by the fall of an apple,” wrote Newton’s friend William Stukeley, quoting a conversation he had with Newton, “as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself.”* But many remain unconvinced that the story is true. After all, Newton only told Stukeley the story a year before he died, and he made no mention of it any other place in his voluminous writings.
然而，毋庸置疑的是，牛顿是第一个意识到，使苹果从树上掉落的力同样支配着月球、地球和太阳的运动——实际上，支配着宇宙中所有物体的运动。这是一个非凡的洞见，但他并没有止步于此。他意识到宇宙中每个物体都吸引着其他物体——并且他提出了一个计算这种吸引力大小的公式，即著名的万有引力定律。该定律指出，两个物体之间的引力与它们的质量乘积成正比，与它们之间距离的平方成反比。
Still, what is unquestionably true is that Newton was the first to realize that the same force that causes an apple to fall from a tree governs the motion of the Moon, the Earth, and the Sun—indeed, of all the objects in the universe. That was an extraordinary insight, but once again, he didn’t stop there. He realized that every object in the universe attracts every other object—and he came up with a formula for calculating just how strong the attraction is, known as his universal law of gravitation. This law states that the force of gravitational attraction between two objects is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them.
换句话说，举一个纯粹假设的例子（我强调这与现实无关），如果地球和木星以相同的距离绕太阳运行，那么由于木星的质量大约是地球的318倍，太阳和木星之间的引力将大约是太阳和地球之间引力的318倍。如果木星和地球的质量相同，但木星的质量大约是地球的318倍，那么太阳和木星之间的引力将大约是地球和太阳之间引力的318倍。如果木星在其实际轨道上，距离太阳的距离大约是地球轨道的五倍，那么由于引力与距离的平方成反比，太阳和地球之间的引力将比太阳和木星之间的引力大二十五倍。
So, in other words, to use a purely hypothetical example, which I stress has no relation to reality, if Earth and Jupiter were orbiting the Sun at the same distance, then because Jupiter is about 318 times more massive than Earth the gravitational force between the Sun and Jupiter would be about 318 times greater than that between the Sun and Earth. And if Jupiter and Earth were the same mass, but Jupiter were in its actual orbit, which is about five times farther from the Sun than the Earth’s orbit, then because the gravitational force is inversely proportional to the square of the distance, it would be twenty-five times greater between the Sun and Earth than between the Sun and Jupiter.
在牛顿于 1687 年出版的著名著作《自然哲学的数学原理》（我们现在称之为《原理》）中，他并没有使用方程式来引入万有引力定律，但这是我们今天在物理学中最常用的表达方式：
In Newton’s famous Philosophiæ Naturalis Principia Mathematica published in 1687—which we now call the Principia—he did not use an equation to introduce the law of universal gravitation, but that’s the way we express it most often in physics today:
这里，F <sub>grav</sub>表示质量分别为m <sub> 1 </sub> 和m <sub> 2 </sub>的物体之间的引力，r表示它们之间的距离；2表示“平方”。G 是什么？它被称为万有引力常数。牛顿当然知道这个常数的存在，但他的《自然哲学的数学原理》中并没有提及。根据之后进行的大量测量，我们现在知道G的最精确值是 6.67428 ± 0.00067 × 10 <sup>-11</sup>。*我们物理学家也相信，正如牛顿所推测的那样，宇宙中的情况都是相同的。
Here, Fgrav is the force of gravitational attraction between an object of mass m1 and one of mass m2, and r is the distance between them; the 2 means “squared.” What is G? That’s what’s called the gravitational constant. Newton knew, of course, that such a constant exists, but it is not mentioned in his Principia. From the many measurements that have since been done, we now know that the most accurate value for G is 6.67428 ± 0.00067 × 10–11.* We physicists also do believe that it’s the same throughout the universe, as Newton conjectured.
牛顿定律的影响巨大，怎么强调都不为过；他的《自然哲学的数学原理》是科学史上最重要的著作之一。他的定律彻底改变了物理学和天文学。他的定律使得计算太阳和行星的质量成为可能。计算方法极其精妙。如果你知道任何行星（例如木星或地球）的公转周期以及它到太阳的距离，你就可以计算出太阳的质量。这听起来是不是很神奇？我们还可以更进一步：如果你知道木星的一颗明亮卫星（伽利略于1609年发现）的公转周期以及木星与这颗卫星之间的距离，你就可以计算出木星的质量。因此，如果你知道月球绕地球的公转周期（27.32天）以及地球与月球之间的平均距离，你就可以计算出木星的质量。如果知道地球距离月球（大约239,000英里），就可以非常精确地计算出地球的质量。我在附录2中会详细解释具体方法。如果你懂一些数学，应该会很喜欢！
The impact of Newton’s laws was gigantic and cannot be overestimated; his Principia is among the most important works of science ever written. His laws changed all of physics and astronomy. His laws made it possible to calculate the mass of the Sun and planets. The way it’s done is immensely beautiful. If you know the orbital period of any planet (say, Jupiter or the Earth) and you know its distance to the Sun, you can calculate the mass of the Sun. Doesn’t this sound like magic? We can carry this one step further; if you know the orbital period of one of Jupiter’s bright moons (discovered by Galileo in 1609) and you know the distance between Jupiter and that moon, you can calculate the mass of Jupiter. Therefore, if you know the orbital period of the Moon around the Earth (it’s 27.32 days) and you know the mean distance between the Earth and the Moon (it’s about 239,000 miles) then you can calculate to a high degree of accuracy the mass of the Earth. I show you how this works in appendix 2. If you can handle some math you may enjoy it!
但牛顿定律的影响远不止于我们的太阳系。它们支配并解释了恒星、双星（第十三章）、星团、星系，甚至星系团的运动，而牛顿定律也为二十世纪暗物质的发现做出了贡献。稍后我会详细阐述这一点。他的定律精妙绝伦——既简洁得令人惊叹，又无比强大。它们解释了许多现象，其阐明的范围之广令人叹为观止。
But Newton’s laws reach far beyond our solar system. They dictate and explain the motion of stars, binary stars (chapter 13), star clusters, galaxies, and even clusters of galaxies, and Newton’s laws deserve credit for the twentieth-century discovery of what we call dark matter. I will tell you more about this later. His laws are beautiful—breathtakingly simple and incredibly powerful at the same time. They explain so much, and the range of phenomena they clarify is mind-boggling.
牛顿将运动物理学、物体间相互作用以及行星运动融会贯通，为天文测量带来了一种全新的秩序，揭示了几个世纪以来纷繁复杂的观测结果是如何相互关联的。其他人也曾瞥见过他这方面的洞见，但却无法像他那样将这些洞见融会贯通。
By bringing together the physics of motion, of interactions between objects, and of planetary movements, Newton brought a new kind of order to astronomical measurements, showing how what had been a jumble of confusing observations made through the centuries were all interconnected. Others had had glimmers of his insights, but they hadn’t been able to put them together as he did.
伽利略在牛顿出生前一年去世，他提出了牛顿第一定律的早期版本，并能用数学描述许多物体的运动。他还发现，所有物体从给定高度下落的速度都相同（在忽略空气阻力的情况下）。然而，他却无法解释为什么会这样。约翰内斯·开普勒推导出了行星轨道运行的基本原理，但他对其中的原理一无所知。牛顿解释了其中的原理。而且，正如我们所看到的，这些答案以及它们引出的许多结论，丝毫没有符合直觉。
Galileo, who died the year before Newton was born, had come up with an early version of Newton’s first law and could describe the motion of many objects mathematically. He also discovered that all objects will fall from a given height at the same speed (in the absence of air drag). He couldn’t, though, explain why it was true. Johannes Kepler had worked out the fundamentals of how planetary orbits worked, but he had no clue why. Newton explained the why. And, as we’ve seen, the answers, and many of the conclusions they lead to, are not in the slightest bit intuitive.
对我来说，运动的力量总是充满魅力。引力无处不在，它遍布宇宙。而它最令人惊叹之处——或者说，最令人惊叹之处之一——在于它的作用距离很远。你有没有认真思考过，我们的星球之所以能保持轨道运行，我们之所以能够生存，是因为相距9300万英里的两个物体之间的吸引力？
The forces of motion are endlessly fascinating to me. Gravity is always with us; it pervades the universe. And the astounding thing about it—well, one astounding thing—is that it acts at a distance. Have you ever really stopped to consider that our planet stays in orbit, that we are all alive because of the attractive force between two objects 93 million miles apart?
运动中的钟摆
Pendulums in Motion
尽管引力在我们生活中无处不在，但它对我们世界的影响方式却常常让我们感到困惑。我经常用摆锤演示来让学生们惊讶地发现，引力的运作方式其实与我们的直觉相悖。以下是它的工作原理。
Even though gravity is a pervasive force in our lives, there are many ways in which the effects it has on our world confound us. I use a pendulum demonstration to surprise students with just how counterintuitively gravity operates. Here’s how it works.
很多人可能认为，如果你在游乐场荡秋千时，旁边的人比你轻得多，比如一个蹒跚学步的孩子，那么你的秋千摆动速度会比他慢得多。但事实并非如此。因此，你可能会惊讶地发现，单摆完成一次摆动所需的时间（我们称之为摆的周期）并不受悬挂在摆锤上的重物（我们称之为摆锤）的影响。请注意，这里我讨论的是所谓的单摆，这意味着它满足两个条件。首先，摆锤的重量必须远大于绳子的重量，以至于绳子的重量可以忽略不计。其次，摆锤的尺寸必须足够小，以至于我们可以将其视为一个点，其尺寸为零。*在家制作一个简单的钟摆很容易：将一个苹果系在一根轻绳的末端，绳子的长度至少是苹果直径的四倍。
Many of you may think that if you swing on a playground swing next to someone who is much lighter than you are, e.g., a toddler, you’ll go much slower than that person. But that is not the case. It may therefore come as a surprise to you that the amount of time it takes to complete one swing of a pendulum, which we call the period of the pendulum, is not affected by the weight hanging from the pendulum (we call this weight the bob). Note that here I’m talking about what’s called a simple pendulum, which means that it meets two conditions. First, the weight of the bob must be so much larger than the weight of the string that the weight of the string can be ignored. Second, the size of the bob needs to be small enough that we can treat it as if it were just a point, which has zero size.* It’s easy to make a simple pendulum at home: attach an apple to the end of a lightweight string that is at least four times longer than the size of the apple.
在课堂上，我运用牛顿运动定律推导出了计算单摆周期的公式，并对其进行了验证。为此，我必须假设单摆摆动的角度很小。让我更详细地解释一下我的意思。当你观察自制的单摆来回摆动时，你会发现大部分时间单摆都在运动，要么向左，要么向右。然而，在一次完整的摆动过程中，单摆会两次静止不动，之后才会反向摆动。当绳子与垂直方向的夹角达到最大值时，摆锤就会停止摆动，我们称之为摆的振幅。如果忽略空气阻力（摩擦力），摆锤在最左侧停止摆动时的最大角度与在最右侧停止摆动时的最大角度相同。我推导出的这个方程只适用于小角度（小振幅）。在物理学中，我们称这种推导为小角度近似。学生们总是问我：“多小才算小？” 有个学生甚至问得非常具体：“5度的振幅算小吗？10度的振幅这个方程还适用吗？或者说10度不算小？” 当然，这些都是很好的问题，我建议我们可以在课堂上进行一次测试。
Using Newton’s laws of motion, I derive in class an equation for calculating the period of a simple pendulum, and then I put the equation to the test. To do that I have to make the assumption that the angle over which the pendulum swings is small. Let me be more precise about what I mean by that. When you look at your homemade pendulum as it swings back and forth, from right to left and from left to right, you will see that most of the time the pendulum is moving, either to the left or to the right. However, there are two times during a complete swing that the pendulum stands still, after which it reverses direction. When this happens the angle between the string and the vertical has reached a maximum value, which we call the amplitude of the pendulum. If air drag (friction) can be ignored, that maximum angle when the pendulum comes to a halt at the far left is the same as when the pendulum comes to a halt at the far right. The equation that I derive is only valid for small angles (small amplitudes). We call such a derivation in physics a small-angle approximation. Students always ask me, “How small is small?” One student is even very specific; she asks, “Is an amplitude of five degrees small? Is the equation still valid for an amplitude of ten degrees or is ten degrees not small?” Of course, those are excellent questions, and I suggest that we will bring this to a test in class.
我推导出的这个方程式非常简单优雅，不过对于那些最近没怎么接触数学的人来说，它可能看起来有点吓人：
The equation that I derive is quite simple and very elegant, though it may look a little daunting to those who haven’t been doing any math lately:
T是摆的周期（单位：秒），L是绳子的长度（单位：米），π 是 3.14，g是重力加速度（9.8 米/秒²）。因此，等式右边可以写成 2π 乘以绳长除以重力加速度的平方根。这里我就不详细解释为什么这个等式是正确的了（如果你想了解推导过程，可以参考我录制的讲座视频；网站链接在第 54 页）。
T is the period of the pendulum (in seconds), L is the length of the string (in meters), π is 3.14, and g is the gravitational acceleration (9.8 meters per second per second). So the right part of the equation reads two π multiplied by the square root of the length of the string divided by the gravitational acceleration. I won’t go into the details here of why this is the correct equation (you can follow the derivation that I do in my recorded lectures if you want to; the website link is on page 54).
我在这里给出这个公式，是为了让您更清楚地了解我的演示是如何精确地验证它的。这个公式预测，长度为1米的单摆周期约为2秒。我测量了用1米长的绳子做单摆完成10次摆动所需的时间，大约是20秒。除以10，就得到了周期2秒。然后我换用绳子长度缩短四分之一的单摆。公式预测周期应该缩短一半。所以我把绳子长度改为25厘米，果然，单摆完成10次摆动大约需要10秒。所以这一切都非常令人信服。
I am giving the equation here so that you can appreciate just how precisely my demonstrations confirm it. The equation predicts that a pendulum 1 meter long has a period of about 2 seconds. I measure the time it takes a pendulum, with a string that long, to complete ten oscillations, and that comes to about 20 seconds. Dividing by 10, we get 2 seconds for the period. Then I go to a pendulum with a string that is four times shorter. The equation predicts that the period should be twice as short. So I make the string 25 centimeters long, and indeed it takes about 10 seconds for ten oscillations. So that is all very reassuring.
为了对这个等式进行比我用手持小苹果摆锤所做的更严谨的检验，我在教室里制作了一个简单的摆锤：一根长5.18米（约17英尺）的绳子，绳子末端系着一个重15公斤的球形钢球。我称它为所有摆锤之母。你可以在我的讲座接近尾声时看到它：http ://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/embed10/ 。
To bring the equation to a much more careful test than what I did with the handheld small apple pendulum, I had a simple pendulum constructed in my classroom: a rope 5.18 meters (about 17 feet) long with a spherical steel bob weighing 15 kilograms at the end of the rope. I call it the mother of all pendulums. You can see it near the end of my lecture here: http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/embed10/.
这个摆的周期T
应该是多少？已知周期 T 为 4.57 秒。为了验证这一点，正如我向学生们承诺的那样，我分别测量了振幅为 5 度和 10 度时的周期。
What should the period, T, of this pendulum be? , which is 4.57 seconds. To bring this to a test, as I promised my students, I measure the period both for a 5-degree and for a 10-degree amplitude.
我使用一个学生能看到的大型数字计时器，它的显示精度可达百分之一秒。多年来，我无数次测试过自己打开和关闭计时器的反应时间，我知道在状态良好的情况下，我的反应时间大约是十分之一秒。这意味着，如果我重复测量同样的周期十几次，得到的周期测量值可能会有0.1秒（甚至0.15秒）的误差。因此，无论我测量一次摆动所需的时间还是十次摆动所需的时间，我的计时结果都会有正负0.1秒的不确定度。所以，我让摆锤摆动十次，因为这样得到的周期值比只摆动一次要精确十倍。
I use a large digital timer that the students can see, and that displays the time to an accuracy of one-hundredth of a second. I’ve tested my reaction time in turning the timer on and off countless times over the years, and I know it’s about one-tenth of a second (on a good day). This means that if I repeat the very same measurement a dozen times I will get measurements for the period that will vary by as much as 0.1 (maybe 0.15) seconds. So whether I measure the time it takes for one oscillation or for ten oscillations, my timing will have an uncertainty of plus or minus 0.1 seconds. I therefore let the pendulum swing ten times, as that will give a ten times more accurate value for the period than if I let it swing only once.
我把摆锤拉出来，使绳子与垂直方向的角度大约为5度，然后松开，开始计时。同学们大声数着摆锤摆动的次数，十次摆动后我停止计时。结果令人惊叹——计时器显示45.70秒，是我预估一次摆动时间的十倍。同学们热烈鼓掌。
I pull the bob out enough so that the angle of the rope with the vertical is about 5 degrees and then let it go and start the timer. The class counts each of the swings out loud, and after ten oscillations I stop the timer. It’s amazing—the timer reads 45.70 seconds, ten times my estimate for one swing. The class applauds wildly.
然后我将振幅增加到 10 度，松开摆锤，开始计时，让全班同学一起数数，数到 10 时，我停止计时：45.75 秒。10 次振荡耗时 45.75 ± 0.1 秒，换算成每次振荡耗时 4.575 ± 0.01 秒。5 度振幅的结果与 10 度振幅的结果相同（在测量误差范围内）。因此，我的公式仍然非常精确。
Then I increase the amplitude to 10 degrees, let the bob go, start the timer, get the class counting, and right at ten, I stop the timer: 45.75 seconds. 45.75 ± 0.1 seconds for ten oscillations translates into 4.575 ± 0.01 seconds per oscillation. The result for the 5-degree amplitude is the same as for the 10-degree amplitude (within the uncertainty of the measurements). So my equation is still very accurate.
然后我问全班同学：“假设我坐在摆锤上，跟着它一起荡——我们得到的周期还会一样吗？还是会改变？”我从来都不喜欢坐在这玩意儿上（真的很疼），但为了科学，为了让学生们开怀大笑、积极参与，我不会错过这个机会。当然，我不能笔直地坐在浮标上，因为那样会缩短绳子的长度，减少摆动的周期。但如果我尽可能地保持身体水平，与浮标处于同一水平线上，就能保持绳子的长度基本不变。所以我把浮标拉起来，放在两腿之间，抓住绳子，然后放手。你可以在这本书的封面上看到这个动作！
Then I ask the class, Suppose I sat on the bob and swung along with it—would we get the same period, or would it change? I never look forward to sitting on this thing (it really hurts), but for science, and to get the students laughing and involved, I wouldn’t miss the opportunity. Of course I can’t sit upright on the bob because that way I will effectively shorten the rope, and reduce the period a bit. But if I make my body as horizontal as possible in order to be at the same level as the bob, I keep the rope length pretty much the same. So I pull the bob up, put it between my legs, grasp the rope, and let myself go. You can see this on the jacket of this book!
对我来说，在不增加反应时间的情况下，一边悬挂在摆锤上一边启动和停止计时器并不容易。不过，我已经练习过无数次了，所以我相当有信心能将测量误差控制在±0.1秒以内。我摆动了十次，学生们大声数着摆动的次数——他们嘲笑我这滑稽的处境，而我则大声抱怨和呻吟——十次摆动后，我关掉计时器，读数是45.61秒。周期是4.56±0.01秒。“物理真管用！”我大喊，学生们都兴奋极了。
It’s not easy for me to start and stop the timer while hanging on the pendulum without increasing my reaction time. However, I’ve practiced this so many times that I am quite sure that I can achieve an uncertainty in my measurements of ± 0.1 seconds. I swing ten times, with students counting the swings out loud—and laughing at the absurdity of my situation while I complain and groan loudly—and when after ten oscillations I turn off the timer, it reads 45.61 seconds. That’s a period of 4.56 ± 0.01 seconds. “Physics works!” I scream, and the students go bananas.
祖母和宇航员
Grandmothers and Astronauts
引力的另一个棘手之处在于，我们可能会被误导，以为它的拉力方向与实际方向不同。引力总是指向地心——当然，这是指地球上的引力，而不是冥王星上的引力。但我们有时会感觉引力是水平方向的，这种我们称之为“人为引力”或“感知引力”的东西，实际上似乎违背了引力本身的规律。
Another tricky aspect of gravity is that we can be fooled into perceiving that it’s pulling from a different direction than it really is. Gravity always pulls toward the center of Earth—on Earth, that is, not on Pluto of course. But we can sometimes perceive that gravity is operating horizontally, and this artificial or perceived gravity, as we call it, can in fact seem to defy gravity itself.
你可以很容易地通过我奶奶每次做沙拉时都会做的一件事来证明这种人造重力。我奶奶有很多奇思妙想——记得吗，她就是教我躺着比站着显得更高的那个人。嗯，她做沙拉的时候可真是乐在其中。她会用漏勺洗生菜，然后不用毛巾擦干（那样会损伤叶子），而是发明了她自己的方法：她把漏勺放在上面，用橡皮筋固定住一块抹布，然后飞快地转圈——我是说真的飞快。
You can demonstrate this artificial gravity easily by doing something my grandmother used to do every time she made a salad. My grandmother had such fantastic ideas—remember, she’s the one who taught me that you’re longer when you’re lying down than when you’re standing up. Well, when she made a salad, she really had a good time. She would wash the lettuce in a colander, and then rather than drying it in a cloth towel, which would damage the leaves, she had invented her own technique: she took the colander and put a dish towel over the top, holding it in place with a rubber band, and then she would swing it around furiously in a circle—I mean really fast.
所以，当我在课堂上演示这个方法时，我会特意提醒前两排的学生合上笔记本，以免纸张被弄湿。我把生菜带到教室，在桌上的水槽里仔细清洗，然后放在滤网里。“准备好了！”我告诉他们，然后用力地在垂直方向上画圈甩动手臂。水珠四处飞溅！当然，现在我们有了乏味的塑料沙拉甩干器来代替我祖母的方法——在我看来，这真是太可惜了。现代生活的很多方面似乎都让生活失去了浪漫的成分。
That’s why when I demonstrate this in class, I make sure to tell the students in the first two rows to close their notebooks so their pages don’t get wet. I bring lettuce into the classroom, wash it carefully in the sink on my table, prepare it in the colander. “Get ready,” I tell them, and I swing my arm vigorously in a vertical circle. Water drops spray everywhere! Now, of course, we have boring plastic salad spinners to substitute for my grandmother’s method—a real pity in my book. So much of modern life seems to take the romance out of things.
宇航员在加速进入地球轨道时也会体验到这种人造重力。我的朋友兼麻省理工学院同事杰弗里·霍夫曼曾五次乘坐航天飞机执行任务，他告诉我，在发射过程中，宇航员会经历一系列不同的加速度，初始加速度约为0.5g ，在固体燃料级结束时达到约2.5g 。之后加速度会短暂下降到约1g，此时液体燃料开始燃烧，加速度再次上升到3g，并在发射的最后一分钟达到峰值——整个过程大约需要八分半钟才能达到约17000英里/小时的速度。这种感觉一点也不舒适。当他们最终进入轨道时，就会失去重量，并感觉像是零重力状态。
This same artificial gravity is experienced by astronauts as they accelerate into orbit around the Earth. A friend and MIT colleague of mine, Jeffrey Hoffman, has flown five missions in the space shuttle, and he tells me that the crew experiences a range of different accelerations in the course of a launch, from about 0.5g initially, building to about 2.5g at the end of the solid fuel stage. Then it drops back down to about 1g briefly, at which point the liquid fuel starts burning, and acceleration builds back up to 3g for the last minute of the launch—which takes about eight and a half minutes total to obtain a speed of about 17,000 miles per hour. And it’s not at all comfortable. When they finally reach orbit they become weightless and they perceive this as zero gravity.
正如你现在所知，无论是生菜感受到滤网的挤压，还是宇航员感受到座椅的挤压，他们都体验到了一种人造重力。我祖母的装置——以及我们常用的沙拉甩干器——当然都是离心机的变体，它们将生菜与附着在叶片上的水分分离，水分会从滤网的孔洞中喷出。你不必成为宇航员也能体验到这种感知到的重力。想想游乐园里那个叫做“旋转飞椅”的刺激项目，你站在一个大型旋转转盘的边缘，背靠着金属围栏。随着转盘越转越快，你会感到越来越被推向围栏，对吧？根据牛顿第三定律，你推墙壁的力与墙壁推你的力大小相等。
As you now know, both the lettuce, feeling the colander pushing against it, and the astronauts, feeling the seats pushing against them, are experiencing a kind of artificial gravity. My grandmother’s contraption—and our salad spinners—are of course versions of a centrifuge, separating the lettuce from the water clinging to its leaves, which shoots out through the colander’s holes. You don’t have to be an astronaut to experience this perceived gravity. Think of the fiendish ride at amusement parks called the Rotor, in which you stand at the edge of a large rotating turntable with your back against a metal fence. As it starts to rotate faster and faster, you feel more and more pushed into the fence, right? According to Newton’s third law, you push on the wall with the same force as the wall pushes on you.
墙壁对你施加的这种力称为向心力。力。它为你提供必要的加速度，使你能够绕圈运动；速度越快，向心力越大。记住，即使速度保持不变，绕圈运动也需要力（因此也需要加速度）。类似地，引力为行星绕太阳运行提供向心力，我在附录2中对此进行了讨论。你推墙的力通常被称为离心力。向心力和离心力大小相等，方向相反。不要混淆两者。只有向心力作用于你（而不是离心力），也只有离心力作用于墙壁（而不是向心力）。
This force with which the wall pushes on you is called the centripetal force. It provides the necessary acceleration for you to go around; the faster you go, the larger is the centripetal force. Remember, if you go around in a circle, a force (and therefore an acceleration) is required even if the speed remains unchanged. In similar fashion, gravity provides the centripetal force on planets to go around the Sun, as I discuss in appendix 2. The force with which you push on the wall is often called the centrifugal force. The centripetal force and the centrifugal force have the same magnitude but in opposite direction. Do not confuse the two. It’s only the centripetal force that acts on you (not the centrifugal force), and it is only the centrifugal force that acts on the wall (not the centripetal force).
有些旋翼机速度极快，甚至可以降低你脚下的地板，而你却不会滑下去。为什么你不会滑下去呢？
Some Rotors can go so fast that they can lower the floor on which you stand and you won’t slide down. Why won’t you slide down?
想想看。如果转子完全不转，重力会使你下滑，因为你和墙壁之间的摩擦力（向上）不足以平衡重力。然而，当地板降低时，转子旋转，摩擦力会增大，因为它取决于向心力。向心力越大（地板降低时），摩擦力也越大。因此，如果地板降低时转子旋转得足够快，摩擦力就能大到足以平衡重力，从而防止你下滑。
Think about it. If the Rotor isn’t spinning at all the force of gravity on you will make you slide down as the frictional force between you and the wall (which will be upward) is not large enough to balance the force of gravity. However, the frictional force, with the floor lowered, will be higher when the Rotor spins, as it depends on the centripetal force. The larger the centripetal force (with the floor lowered), the larger the frictional force. Thus, if the Rotor spins fast enough with the floor lowered, the frictional force can be large enough that it will balance the force of gravity and thus you won’t slide down.
有很多方法可以演示人造重力。这里有一个你可以在家尝试的方法；确切地说，是在你家后院。把绳子系在一个空油漆罐的把手上，然后往罐子里装满水——我建议装半罐，否则罐子会非常重，难以旋转——接着用尽全力把罐子举过头顶，绕圈甩动。你可能需要练习几次才能甩得足够快。一旦你掌握了技巧，你会发现罐子里的水一滴都不会漏出来。我在课堂上让学生们做这个实验，我必须说，这真是太有趣了！这个小实验也解释了为什么有些特别危险的旋转器会逐渐翻转，直到你完全倒立，但你仍然能感觉到重力。不要掉到地上（当然，为了安全起见，你也被绑在了上面）。
There are lots of ways to demonstrate artificial gravity. Here’s one you can try at home; well, in your backyard. Tie a rope to the handle of an empty paint can and fill the can with water—about half full, I’d say, otherwise it will be awfully heavy to spin—and then whip the can around as hard as you can up over your head in a circle. It might take some practice to get it going fast enough. Once you do, you’ll see that not a drop of water will fall out. I have students do this in my classes, and I must say it’s a complete riot! This little experiment also explains why, with some especially pernicious versions of the Rotor, it will gradually turn over until you are completely upside down at one point, and yet you don’t drop down to the ground (of course, for safety’s sake, you are also strapped into the thing).
秤对我们施加的力决定了秤显示的体重；使宇航员处于失重状态的是引力，而不是引力的缺失；当苹果落向地球时，地球也随之落向苹果。牛顿定律简洁明了，影响深远，意义深远，却又完全违反直觉。在推导出他著名的定律时，艾萨克·牛顿爵士面对的是一个真正神秘的宇宙，而我们都因他解开其中一些谜团的能力而受益匪浅，并以一种全新的视角看待我们的世界。
The force with which a scale pushes on us determines what the scale tells us we weigh; it’s the force of gravity—not the lack of it—that makes astronauts weightless; and when an apple falls to Earth, the Earth falls to the apple. Newton’s laws are simple, far-reaching, profound, and utterly counterintuitive. In working out his famous laws, Sir Isaac Newton was contending with a truly mysterious universe, and we have all benefited enormously from his ability to unlock some of these mysteries and to make us see our world in a fundamentally new way.
第四章
CHAPTER 4
用吸管喝饮料的魔力
The Magic of Drinking with a Straw
我最喜欢的课堂演示之一是用两个油漆罐和一支步枪。我把一个油漆罐装满水，然后盖紧盖子。接着，我把第二个油漆罐装到几乎满，但罐口下方留出一英寸左右的空间，也盖好盖子。我把两个罐子前后摆放在桌子上，然后走到几码外的另一张桌子旁，桌子上放着一个长长的白色木箱，显然里面装着某种装置。我掀开箱子，露出一支固定在支架上的步枪，枪口正对着油漆罐。学生们瞪大了眼睛——我要在课堂上开枪吗？
One of my favorite in-class demonstrations involves two paint cans and a rifle. I fill one can to the rim with water and then bang the top on tightly. Then I fill the second can most of the way, but leaving an inch or so of space below the rim, and also seal that one. After placing them one in front of the other on a table, I walk over to a second table several yards away, on which rests a long white wooden box, clearly covering some kind of contraption. I lift up the box, revealing a rifle fastened onto a stand, pointing at the paint cans. The students’ eyes widen—am I going to fire a rifle in class?
“如果我们用子弹射穿这些油漆罐，会发生什么？”我问他们。我没等他们回答，就弯下腰检查步枪的瞄准情况，通常还会稍微摆弄一下枪栓。这样做能营造紧张气氛。我吹掉枪膛里的灰尘，装上一颗子弹，然后宣布：“好了，子弹上膛了。准备好了吗？”接着，我站在步枪旁，手指放在扳机上，数着“三、二、一”——扣动扳机。一个油漆罐的盖子瞬间高高弹起，而另一个却纹丝不动。你觉得哪个罐子的盖子会掉下来？
“If we were to shoot a bullet through these paint cans, what would happen?” I ask them. I don’t wait for answers. I bend down to check the rifle’s aim, usually fiddling with the bolt a little. This is good for building up tension. I blow some dust out of the chamber, slide a bullet in, and announce, “All right, there goes the bullet. Are we ready for this?” Then standing alongside the rifle, I put my finger on the trigger, count “Three, two, one”—and fire. One paint can’s top instantly pops way up into the air, while the other one stays put. Which can do you think loses its top?
要知道答案，首先必须知道空气是可压缩的。水则不然；空气分子可以被压缩得更紧密，任何气体的分子都可以，但水分子——以及任何液体的分子——都不能。改变液体的密度需要极其巨大的力和压力。现在，当子弹射入油漆罐时，它会带来巨大的压力。在装满空气的罐子里，空气就像一个缓冲垫或减震器，所以水不会受到干扰，罐子也不会爆炸。但在装满水的罐子里，水无法被压缩。因此，子弹在水中产生的额外压力会对罐壁和罐顶施加很大的力，导致罐顶被炸开。你可以想象，这场面非常震撼，我的学生们总是被吓得不轻。
To know the answer, you first have to know that air is compressible and water isn’t; air molecules can be squished closer in toward one another, as can the molecules of any gas, but those of water—and of any liquid at all—cannot. It takes horrendous forces and pressures to change the density of a liquid. Now, when the bullet enters the paint cans, it brings a great deal of pressure with it. In the can with the air in it, the air acts like a cushion, or a shock absorber, so the water isn’t disturbed and the can doesn’t explode. But in the can full of water, the water can’t compress. So the extra pressure the bullet introduces in the water exerts a good deal of force on the walls and on the top of the can and the top blows off. As you may imagine, it’s really very dramatic and my students are always quite shocked.
被气压包围
Surrounded by Air Pressure
在课堂上，我总是喜欢用压力这个话题来活跃气氛，而气压尤其有趣，因为它有很多违反直觉的地方。我们甚至在真正去寻找它之前，都不会意识到自己正承受着气压，而一旦意识到它的存在，就会觉得非常神奇。一旦我们意识到它的存在——并开始了解它——我们就会发现它无处不在，从气球到气压计，从吸管的工作原理到你能在海洋中游泳和浮潜的深度，都与它息息相关。
I always have a lot of fun with pressure in my classes, and air pressure is particularly entertaining because so much is so counterintuitive about it. We don’t even realize we are experiencing air pressure until we actually look for it, and then it’s just astonishing. Once we realize it’s there—and begin to understand it—we begin to see evidence for it everywhere, from balloons to barometers, to why a drinking straw works, to how deep you can swim and snorkel in the ocean.
那些我们起初看不见、习以为常的事物，比如重力和气压，最终却往往是最令人着迷的现象之一。这就像那个笑话：两条鱼在河里快乐地游来游去。其中一条鱼转过头，一脸怀疑地问另一条：“你们都在谈论‘水’吗？”
The things we don’t see at first, and take for granted, like gravity and air pressure, turn out to be among the most fascinating of all phenomena. It’s like the joke about two fish swimming along happily in a river. One fish turns to the other, a skeptical look on its face, and says, “What’s all this new talk about ‘water’?”
在我们看来，我们理所当然地认为看不见的大气层的重量和密度是理所当然的。事实上，我们生活在一片浩瀚的空气海洋的底部，它每时每刻都在对我们施加巨大的压力。假设我伸出手，掌心向上。现在想象一下，一根很长的方形管子，每边宽1厘米（当然，是边长），平衡地放在我的手上，一直上升到大气层的顶部。这超过一百英里。光是空气的重量就足以压在我们身上。管子本身——先不说管子——大约重 1 公斤，也就是大约 2.2 磅。*这是测量气压的一种方法：每平方厘米1.03千克的压力被称为标准大气压。（您可能也知道它大约是每平方英寸14.7磅。）
In our case, we take the weight and density of our invisible atmosphere for granted. We live, in truth, at the bottom of a vast ocean of air, which exerts a great deal of pressure on us every second of every day. Suppose I hold my hand out in front of me, palm up. Now imagine a very long piece of square tubing that is 1 centimeter wide (on each side, of course) balanced on my hand and rising all the way to the top of the atmosphere. That’s more than a hundred miles. The weight of the air alone in the tube—forget about the tubing—would be about 1 kilogram, or about 2.2 pounds.* That’s one way to measure air pressure: 1.03 kilograms per square centimeter of pressure is called the standard atmosphere. (You may also know it as about 14.7 pounds per square inch.)
计算气压（以及任何其他类型的压力）的另一种方法是使用一个相当简单的公式，这个公式非常简单，以至于我直接用文字描述出来而没有说明它是公式。压力等于力除以面积：P = F / A。因此，海平面的气压约为每平方厘米1千克。以下是另一种形象化理解力、压力和面积之间关系的方法。
Another way to calculate air pressure—and any other kind of pressure—is with a fairly simple equation, one so simple that I’ve actually just put it in words without saying it was an equation. Pressure is force divided by area: P = F/A. So, air pressure at sea level is about 1 kilogram per square centimeter. Here’s another way to visualize the relationship between force, pressure, and area.
假设你在池塘上滑冰，有人掉进了洞里。你会怎么做？直接走过去吗？不，你应该趴在冰面上，慢慢地向前挪动，这样可以分散身体对冰面的压力，减少冰面破裂的可能性。站立和躺卧时冰面受力的差异非常显著。
Suppose you are ice-skating on a pond and someone falls through. How do you approach the hole—by walking on the ice? No, you get down on your stomach and slowly inch forward, distributing the force of your body on the ice over a larger area, so that you put less pressure on the ice, making it much less likely to break. The difference in pressure on the ice when standing versus lying down is remarkable.
假设你体重70公斤，双脚稳稳地站在冰面上。如果你的双脚接触面积约为500平方厘米（0.05平方米），那么你施加的压力为每平方米70/0.05公斤，即每平方米1400公斤。如果你抬起一只脚，压力就会翻倍，达到每平方米2800公斤。如果你像我一样身高约1.83米，然后躺在冰面上，会发生什么呢？你70公斤的体重分散到约8000平方厘米（约0.8平方米）的冰面上，你的身体施加的压力仅为每平方米87.5公斤，大约比你单脚站立时小32倍。接触面积越大，压力越小；反之，接触面积越小，压力越大。压力的很多特性都与直觉相悖。
Say you weigh 70 kilograms and are standing on ice with two feet planted. If your two feet have a surface area of about 500 square centimeters (0.05 square meters), you are exerting 70/0.05 kilograms per square meter of pressure, or 1,400 kilograms per square meter. If you lift up one foot, you will have doubled the pressure to 2,800 kilograms per square meter. If you are about 6 feet tall, as I am, and lie down on the ice, what happens? Well, you spread the 70 kilograms over about 8,000 square centimeters, or about 0.8 square meters, and your body exerts just 87.5 kilograms per square meter of pressure, roughly thirty-two times less than while you were standing on one foot. The larger the area, the lower the pressure, and, conversely, the smaller the area, the larger the pressure. Much about pressure is counterintuitive.
例如，压力本身没有方向。然而，压力产生的力是有方向的；它垂直于压力作用面。作用力。现在伸出你的手（掌心向上），想想作用在你手上的力——不再考虑管子的作用。我的手掌面积大约是150平方厘米，所以一定有一个150公斤（约330磅）的力向下压着它。那么，为什么我能如此轻松地举起它呢？毕竟，我又不是举重运动员。事实上，如果这是唯一的力，你不可能用手举起这么重的重量。但还有更多因素。由于空气压力从四面八方包围着我们，你的手背上也存在一个330磅的向上力。因此，作用在你手上的合力为零。
For example, pressure has no direction. However, the force caused by pressure does have a direction; it’s perpendicular to the surface the pressure is acting on. Now stretch out your hand (palm up) and think about the force exerted on your hand—no more tube involved. The area of my hand is about 150 square centimeters, so there must be a 150-kilogram force, about 330 pounds, pushing down on it. Then why am I able to hold it up so easily? After all, I’m no weight lifter. Indeed, if this were the only force, you would not be able to carry that weight on your hand. But there is more. Because the pressure exerted by air surrounds us on all sides, there is also a force of 330 pounds upward on the back of your hand. Thus the net force on your hand is zero.
但为什么在如此巨大的压力下，你的手却不会被压碎呢？显然，你手上的骨头足够坚固，不会被压碎。拿一块和你手掌大小一样的木头来，它肯定不会被大气压力压碎。
But why doesn’t your hand get crushed if so much force is pressing in on it? Clearly the bones in your hand are more than strong enough not to get crushed. Take a piece of wood of the size of your hand; it’s certainly not getting crushed by the atmospheric pressure.
但我的胸部呢？它的面积大约为1000平方厘米。因此，由于气压作用在其上的合力约为1000千克，也就是1吨。作用在我背部的合力也约为1吨。为什么我的肺不会塌陷？原因是肺内的气压也是1个大气压；因此，肺内空气与作用在胸部的外部空气之间没有压力差。这就是我能轻松呼吸的原因。拿一个和你的胸部大小相近的纸板箱、木箱或金属箱。把箱子盖上。箱子里的空气就是你呼吸的空气——1个大气压。箱子不会被压扁，原因和你的肺不会塌陷的原因一样。房屋不会在大气压下倒塌，因为房屋内外的气压相同；我们称之为压力平衡。如果箱子（或房屋）内的气压远低于1个大气压，情况就会截然不同；很有可能它会被压碎，就像我在课堂上演示的那样。稍后会详细讲解。
But how about my chest? It has an area of about 1,000 square centimeters. Thus the net force exerted on it due to air pressure is about 1,000 kilograms: 1 metric ton. The net force on my back would also be about 1 ton. Why don’t my lungs collapse? The reason is that inside my lungs the air pressure is also 1 atmosphere; thus, there is no pressure difference between the air inside my lungs and the outside air pushing down on my chest. That’s why I can breathe easily. Take a cardboard or wooden or metal box of similar dimensions as your chest. Close the box. The air inside the box is the air you breathe—1 atmosphere. The box does not get crushed for the same reason that your lungs will not collapse. Houses do not collapse under atmospheric pressure because the air pressure inside is the same as outside; we call this pressure equilibrium. The situation would be very different if the air pressure inside a box (or a house) were much lower than 1 atmosphere; chances are it would then get crushed, as I demonstrate in class. More about this later.
我们通常不会注意到气压，但这并不意味着它对我们不重要。毕竟，天气预报总是会提到高低气压系统。我们都知道，高气压系统往往会带来晴朗的好天气，而低气压系统则意味着某种风暴锋面即将到来。因此，测量气压至关重要。我们非常想了解气压——但如果我们感觉不到它，我们该如何了解呢？你可能知道我们用气压计来测量，但这当然无法解释很多问题。
The fact that we don’t normally notice air pressure doesn’t mean it’s not important to us. After all, weather forecasts are constantly referring to low-and high-pressure systems. And we all know that a high-pressure system will tend to bring nice clear days, and a low-pressure system means some kind of storm front is approaching. So measuring air pressure is something we very much want to do—but if we can’t feel it, how do we do that? You may know that we do it with a barometer, but of course that doesn’t explain much.
吸管的魔力
The Magic of Straws
我们先来看一个你可能已经做过几十次的小技巧。如果你把吸管插进一杯水里——或者像我在课堂上喜欢做的那样，插进一杯蔓越莓汁里——吸管就会被果汁充满。然后，如果你用手指堵住吸管口，开始把它从杯子里拉出来，果汁就会留在吸管里；简直就像变魔术一样。这是为什么呢？解释起来可没那么简单。
Let’s begin with a little trick that you’ve probably done dozens of times. If you put a straw into a glass of water—or as I like to do in class, of cranberry juice—it fills up with juice. Then, if you put a finger over the top of the straw and start pulling it out of the glass, the juice stays in the straw; it’s almost like magic. Why is this? The explanation is not so simple.
为了解释其工作原理（这将有助于我们理解气压计），我们需要了解液体中的压力。仅由液体产生的压力称为静水压力（“静水压力”一词源于拉丁语，意为“静止的液体”）。请注意，液体表面以下（例如海洋）的总压力是水面以上大气压力（例如你伸出的手所感受到的压力）和静水压力的总和。现在，这里有一个基本原理：在静止的液体中，相同高度处的压力相同。因此，在水平面上，压力处处相等。
In order to explain how this works, which will help us get to a barometer, we need to understand pressure in liquids. The pressure caused by liquid alone is called hydrostatic pressure (“hydrostatic” is derived from the Latin for “liquid at rest”). Note that the total pressure below the surface of a liquid—say, the ocean—is the total of the atmospheric pressure above the water’s surface (as with your outstretched hand) and the hydrostatic pressure. Now here’s a basic principle: In a given liquid that is stationary, the pressure is the same at the same levels. Thus the pressure is everywhere the same in horizontal planes.
所以，如果你在游泳池里，把手放在浅水区水面下1米处，你手上的总压力（即大气压（1个大气压）和静水压力之和）与你朋友在深水区水面下1米处所受的压力相同。但是，如果你把手放到水面下2米处，它所受到的静水压力就会增加一倍。水面以上的液体越多，该处的静水压力就越大。
So if you are in a swimming pool, and you put your hand 1 meter below the surface of the pool at the shallow end, the total pressure on your hand, which is the sum of the atmospheric pressure (1 atmosphere) and the hydrostatic pressure, will be identical to the pressure on your friend’s hand, also at 1 meter below the surface, at the deep end of the pool. But if you bring your hand down to 2 meters below the surface, it will experience a hydrostatic pressure that is twice as high. The more fluid there is above a given level, the greater the hydrostatic pressure at that level.
顺便说一句，同样的原理也适用于气压。我们有时会把大气层比作一片空气海洋，在这片海洋的底部，也就是地球表面的大部分区域，气压约为1个大气压。但如果我们站在一座非常高的山峰上，气压就会……上方空气较少，因此大气压也较低。在珠穆朗玛峰顶，大气压只有大约三分之一。
The same principle holds true for air pressure, by the way. Sometimes we talk about our atmosphere as being like an ocean of air, and at the bottom of this ocean, over most of Earth’s surface, the pressure is about 1 atmosphere. But if we were on top of a very tall mountain, there would be less air above us, so the atmospheric pressure would be less. At the summit of Mount Everest, the atmospheric pressure is only about one third of an atmosphere.
如果由于某种原因，水平面上的压力不均匀，那么液体就会流动，直到水平面上的压力达到平衡。空气也是如此，我们称之为风——空气从高压区流向低压区以平衡压力差，当压力达到平衡时，这种现象就会停止。
Now, if for some reason the pressure is not the same in a horizontal plane, then the liquid will flow until the pressure in the horizontal plane is equalized. Again, it’s the same with air, and we know the effect as wind—it’s caused by air moving from high pressure to low pressure to even out the differences, and it stops when the pressure is equalized.
那么吸管里发生了什么？当你把吸管放入液体中时——现在吸管顶部是开口的——液体会进入吸管，直到吸管表面与吸管外玻璃杯中液体的表面齐平；两个表面的压力相同：1 个大气压。
So what’s happening with the straw? When you lower a straw into liquid—for now with the straw open at the top—the liquid enters the straw until its surface reaches the same level as the surface of the liquid in the glass outside the straw; the pressure on both surfaces is the same: 1 atmosphere.
现在假设我吸吮吸管。我会吸出一些空气，这会降低吸管内液体上方空气柱的压力。如果吸管内的液体保持原位，那么液体表面的压力就会低于1个大气压，因为液体上方的空气压力降低了。这样一来，吸管内外两个处于同一水平面（同一水平面）的表面压力就会不同，这是不允许的。因此，吸管内的液体会上升，直到与吸管外表面处于同一水平面的液体压力再次达到1个大气压。如果我通过吸吮使吸管内的空气压力降低了1%（即从1.00个大气压降至0.99个大气压），那么我们能想到的几乎任何一种饮料——水、蔓越莓汁、柠檬水、啤酒或葡萄酒——都会上升大约10厘米。我怎么知道的呢？
Now suppose I suck on the straw. I will take some of the air out of it, which lowers the pressure of the column of air above the liquid inside the straw. If the liquid inside the straw remained where it was, then the pressure at its surface would become lower than 1 atmosphere, because the air pressure above the liquid has decreased. Thus the pressure on the two surfaces, inside and outside the straw, which are at the same level (in the same horizontal plane) would differ, and that is not allowed. Consequently, the liquid in the straw rises until the pressure in the liquid inside the straw at the same level as the surface outside the straw again becomes 1 atmosphere. If by sucking, I lower the air pressure in the straw by 1 percent (thus from 1.00 atmosphere to 0.99 atmosphere) then just about any liquid we can think of drinking—water or cranberry juice or lemonade or beer or wine—would rise about 10 centimeters. How do I know?
吸管中的液体必须上升，才能弥补液体上方0.01个大气压的气压损失。根据计算液体静水压力的公式（这里我就不赘述了），我知道水（或任何密度相近的液体）0.01个大气压的静水压力是由10厘米高的液柱产生的。
Well, the liquid in the straw has to rise to make up for the 0.01-atmosphere loss of air pressure above the liquid in the straw. And from the formula for calculating the hydrostatic pressure in a liquid, which I won’t go into here, I know that a hydrostatic pressure of 0.01 atmosphere for water (or for any comparably dense liquid) is created by a column of 10 centimeters.
如果你的吸管长度是20厘米，你就得吸要让果汁上升20厘米到达你的嘴边，就需要将气压降低到0.98个大气压。记住这一点，后面会用到。现在你已经了解了航天飞机中的失重状态（第三章）以及吸管的工作原理（本章），我这里有一个有趣的问题：一团果汁漂浮在航天飞机上。由于果汁处于失重状态，所以不需要杯子。一名宇航员小心地将一根吸管插入果汁团中，然后开始吸吮。他能用这种方式喝到果汁吗？你可以假设航天飞机内的气压约为1个大气压。
If the length of your straw was 20 centimeters, you would have to suck hard enough to lower the air pressure to 0.98 atmosphere in order for the juice to rise 20 centimeters and reach your mouth. Keep this in mind for later. Now that you know all about weightlessness in the space shuttle (chapter 3) and about how straws work (this chapter), I have an interesting problem for you: A ball of juice is floating in the shuttle. A glass is not needed as the juice is weightless. An astronaut carefully inserts a straw into the ball of juice, and he starts sucking on the straw. Will he be able to drink the juice this way? You may assume that the air pressure in the shuttle is about 1 atmosphere.
现在回到刚才用手指按住吸管顶部的例子。如果你慢慢地将吸管向上提起，比如5厘米（约2英寸），只要吸管仍然浸在果汁里，果汁就不会从吸管里流出来。事实上，果汁几乎（但并非完全）会停留在之前的位置。你可以在提起吸管之前，在吸管侧面果汁液面的位置做个标记来验证这一点。提起吸管后，吸管内果汁液面的高度会比杯子里果汁液面的高度高出大约5厘米。
Now back to the case of the straw with your finger on top. If you raise the straw slowly up, say 5 centimeters, or about 2 inches, as long as the straw is still in the juice, the juice will not run out of the straw. In fact it will almost (not quite) stay exactly at the mark where it was before. You can test this by marking the side of the straw at the juice line before you lift it. The surface of the juice inside the straw will now be about 5 centimeters higher than the surface of the juice in the glass.
但鉴于我们之前关于吸管内外压力在同一水平面上达到平衡的神圣论断，这怎么可能呢？这难道不违反规则吗？不，并没有！大自然非常巧妙；手指夹在吸管里的空气体积会略微增大，使其压力恰好降低（约0.005个大气压），从而使吸管内液体在同一水平面上的压力与杯中液体表面的压力相同：1个大气压。这就是为什么果汁不会正好上升5厘米，而是略少一点，也许只少1毫米——这恰好足以让空气获得足够的额外体积，使其压力降低到所需的数值。
But given our earlier sacred statement about the pressure equalizing inside and outside of the straw—at the same level—how can this be? Doesn’t this violate the rule? No it does not! Nature is very clever; the air trapped by your finger in the straw will increase its volume just enough so that its pressure will decrease just the right amount (about 0.005 atmosphere) so that the pressure in the liquid in the straw at the same level of the surface of the liquid in the glass becomes the same: 1 atmosphere. This is why the juice will not rise precisely 5 centimeters, but rather just a little less, maybe only 1 millimeter less—just enough to give the air enough extra volume to lower its pressure to the desired amount.
你能猜到当你把管子一端封住，然后慢慢向上提拉时，水（在海平面）能上升多高吗？这取决于你开始提拉时管子里有多少空气。如果吸管里几乎没有空气，或者更好的是完全没有空气，那么水能上升的最大高度大约是34英尺——略高于10米。当然，你不可能用一根小吸管做到这一点。玻璃管当然可以，但一桶水也行。这让你感到惊讶吗？更令人难以置信的是，管子的形状并不重要。你可以让它扭曲，甚至变成螺旋状，水仍然可以达到34英尺的垂直高度，因为34英尺高的水会产生1个大气压的静水压力。
Can you guess how high water (at sea level) can go in a tube when you’ve closed off one end and you slowly raise the tube upward? It depends on how much air was trapped inside the tube when you started raising it. If there was very little air in the straw, or even better no air at all, the maximum height the water could go would be about 34 feet—a little more than 10 meters. Of course, you couldn’t do this with a small glass, but a bucket of water might do. Does this surprise you? What makes it even more difficult to grasp is that the shape of the tube doesn’t matter. You could make it twist and even turn it into a spiral, and the water can still reach a vertical height of 34 feet, because 34 feet of water produces a hydrostatic pressure of 1 atmosphere.
已知大气压越低，水柱的最大高度也越低，这为我们提供了一种测量大气压的方法。为了验证这一点，我们可以驱车前往华盛顿山顶（海拔约6300英尺），那里的大气压约为0.82个大气压。这意味着管外水面的压力不再是1个大气压，而是约0.82个大气压。因此，当我在管外水面高度测量管内水压时，压力也必须为0.82个大气压，从而导致水柱的最大高度降低。管内水柱的最大高度将为0.82乘以34英尺，约为28英尺。
Knowing that the lower the atmospheric pressure, the lower the maximum possible column of water will be, provides us with a way to measure atmospheric pressure. To see this, we could drive to the top of Mount Washington (about 6,300 feet high), where the atmospheric pressure is about 0.82 atmosphere, so this means that the pressure at the surface outside the tube is no longer 1 atmosphere but only about 0.82 atmosphere. So, when I measure the pressure in the water inside the tube at the level of the water surface outside the tube, it must also be 0.82 atmosphere, and thus the maximum possible height of the water column will be lower. The maximum height of water in the tube would then be 0.82 times 34 feet, which is about 28 feet.
如果我们用蔓越莓汁测量液柱的高度，并在管子上标记米和厘米，我们就制作了一个蔓越莓汁气压计——它可以指示气压的变化。顺便一提，据说法国科学家布莱兹·帕斯卡曾用红酒制作过气压计，这或许并不令人意外，毕竟他是一位法国人。而被认为是17世纪中期气压计发明者的意大利人埃万杰利斯塔·托里切利，曾短暂担任伽利略的助手，最终选择了水银作为气压计的介质。这是因为，对于给定的液柱高度，密度较大的液体产生的静水压力更大，因此它们在管子中上升的高度也更短。水银的密度大约是水的13.6倍，这使得测量管子的长度更加方便。 34 英尺高的水柱（即 1 个大气压）的静水压力等于 34 英尺除以 13.6，即 2.5 英尺汞柱（2.5 英尺等于 30 英寸或 76 厘米）。
If we measure the height of that column using cranberry juice by marking meters and centimeters on the tube, we have created a cranberry juice barometer—which will indicate changes in air pressure. The French scientist Blaise Pascal, by the way, is said to have made a barometer using red wine, which is perhaps to be expected of a Frenchman. The man credited with inventing the barometer in the mid-seventeenth century, the Italian Evangelista Torricelli, who was briefly an assistant to Galileo, settled eventually on mercury for his barometer. This is because, for a given column, denser liquids produce more hydrostatic pressure and so they have to rise less in the tube. About 13.6 times denser than water, mercury made the length of the tube much more convenient. The hydrostatic pressure of a 34-foot column of water (which is 1 atmosphere) is the same as 34 feet divided by 13.6 which is 2.5 feet of mercury (2.5 feet is 30 inches or 76 centimeters).
托里切利最初并非试图用他的装置测量气压。他想弄清楚的是，吸水泵能抽取的水柱高度是否存在极限——这是一个严重的问题。在灌溉实验中，他将水银倒入一根约1米长、底部封闭的玻璃管中，直至管口。然后，他用拇指封住管口，将玻璃管倒置，浸入盛有水银的碗中，同时移开拇指。此时，部分水银从玻璃管流回碗中，但剩余的水银柱高度约为76厘米。他认为，管口的空隙是真空，这是实验室中最早产生的真空之一。他知道水银的密度约为水的13.6倍，因此可以计算出水银柱的最大高度——这才是他真正想知道的——约为34英尺。在计算过程中，他还意外地注意到液面会随着时间推移而升降，并由此推断，这种变化是由大气压力的变化引起的。真是妙计！他的实验解释了为什么水银气压计的管顶总会留有一些额外的真空空间。
Torricelli wasn’t actually trying to measure air pressure at first with his device. He was trying to find out whether there was a limit to how high suction pumps could draw up a column of water—a serious problem in irrigation. He poured mercury to the top of a glass tube about 1 meter long, closed at the bottom. He then sealed the opening at the rim with his thumb and turned it upside down, into a bowl of mercury, taking his thumb away. When he did this, some of the mercury ran out of the tube back into the bowl, but the remaining column was about 76 centimeters high. The empty space at the top of the tube, he argued, was a vacuum, one of the very first vacuums produced in a laboratory. He knew that mercury was about 13.6 times denser than water, so he could calculate that the maximum length of a water column—which was what he really wanted to know—would be about 34 feet. While he was working this out, as a side benefit, he noticed that the level of the liquid rose and fell over time, and he came to believe that these changes were due to changes in atmospheric pressure. Quite brilliant. And his experiment explains why mercury barometers always have a little extra vacuum space at the top of their tubes.
水下压力
Pressure Under Water
托里切利通过计算水柱的最大高度，也解答了你可能在海里试图一睹鱼儿风采时曾思考过的问题。我猜你这辈子大概尝试过浮潜吧。不过，大多数浮潜呼吸管的长度都不超过一英尺；我相信你肯定也曾想过潜得更深一些，希望呼吸管能更长一些。你觉得你能潜多深，呼吸管还能正常工作呢？五英尺？十英尺？二十英尺？
By figuring out the maximum height of a column of water, Torricelli also figured out something you may have thought about while trying to catch a glimpse of fish in the ocean. My hunch is you’ve probably tried snorkeling at some point in your life. Well, most snorkels have tubes no more than a foot long; I’m sure you’ve wanted to go deeper at times and wished the snorkel were longer. How deep do you think you could go and still have the snorkel work? Five feet, ten feet, twenty?
我喜欢在课堂上用一种叫做压力计的简单装置来解答这个问题；压力计是实验室里常见的设备。它非常简单，你也可以在家轻松制作一个，我稍后会详细介绍。我真正想知道的是，我能潜到水面以下多深还能吸气。为了弄清楚这一点，我们需要测量水压作用在我胸口的静水压力，越往下潜，这个压力就越大。
I like to find the answer to this question in class with a simple device called a manometer; it’s a common piece of lab equipment. It’s very simple, and you could easily make one at home, as I’ll describe in just a bit. What I really want to find out is how deep I can be below the surface and still suck air into my lungs. In order to figure this out, we have to measure the hydrostatic pressure of the water bearing in on my chest, which gets more powerful the deeper I go.
我们周围的压力，记住，是完全相同的。水压是大气压力和静水压力的总和。如果我潜入水下，我会吸入外界空气，这些空气的压力为1个大气压。因此，当我通过呼吸管吸气时，肺部空气的压力也变为1个大气压。但是，胸部的压力是大气压力加上静水压力。所以，胸部的压力高于肺部压力，两者之差恰好就是静水压力。这不会影响呼气，但吸气时，我必须扩张胸腔。如果因为潜得太深导致静水压力过高，我就没有足够的肌肉力量来克服压力差，也就无法吸入更多空气。这就是为什么如果我想潜得更深，就需要吸入加压空气来克服静水压力的原因。但是高压空气对我们的身体来说负担很重，所以潜水时间有严格的限制。
The pressure surrounding us, which is, remember, identical at identical levels, is the sum of the atmospheric pressure and the hydrostatic pressure. If I snorkel below the surface of the water, I breathe in air from the outside. That air has a pressure of 1 atmosphere. As a result, when I take air in through the snorkel, the pressure of the air in my lungs becomes the same, 1 atmosphere. But the pressure on my chest is the atmospheric pressure plus the hydrostatic pressure. So now the pressure on my chest is higher than the pressure inside my lungs; the difference is exactly the hydrostatic pressure. This causes no problem in exhaling, but when I inhale, I have to expand my chest. And if the hydrostatic pressure is too high because I’m too deep in the water, I simply don’t have the muscular strength to overcome the pressure difference, and I can’t take in more air. That’s why, if I want to go deeper in the water, I need to breathe in pressurized air to overcome the hydrostatic pressure. But highly pressurized air is quite taxing on our bodies, which is why there are strict limits to the amount of time for dives.
现在回到浮潜的话题，我能潜多深呢？为了弄清楚这一点，我在阶梯教室的墙上安装了一个压力计。想象一下一根大约4米长的透明塑料管。我把一端固定在左侧墙上，然后把它弯成一个U形。U形的每个臂都略小于2米长。我往管子里倒入大约2米长的蔓越莓汁，它自然地在U形管的两侧达到相同的高度。现在，我对着管子的右端吹气，把蔓越莓汁推到U形管左侧。我能把蔓越莓汁推上去的垂直距离就代表了我能潜多深。为什么呢？因为这衡量的是我的肺部能施加多大的压力来克服水的静水压力——在这个实验中，蔓越莓汁和水是等效的——但蔓越莓汁更容易被学生们看到。
Now to come back to snorkeling, how far down can I go? To figure this out, I rig a manometer up on the wall of the lecture hall. Imagine a transparent plastic tube about 4 meters long. I attach one end to the wall high up on the left and then snake it into a U shape on the wall. Each arm of the U is a little less than 2 meters long. I pour about 2 meters’ worth of cranberry juice into the tube and it naturally settles to the same level on each side of the U tube. Now, by blowing into the right end of the tube I push the cranberry juice up on the left side of the U tube. The vertical distance I can push the juice up will tell me how deep I will be able to snorkel. Why? Because this is a measure of how much pressure my lungs can apply to overcome the hydrostatic pressure of the water—cranberry juice and water being for this purpose equivalent—but the cranberry juice is easier to see for the students.
我俯身，完全呼气，吸气充满肺部，将管子的右端含入口中，使劲吹气。我的脸颊凹陷，眼睛瞪得老大，果汁沿着U形管的左侧缓缓上升，最终只上升了——你猜对了——50厘米。我使尽浑身解数才把它吹到那里，而且我憋气的时间也超过……几秒钟后，我把左侧的果汁向上推了50厘米，这意味着我也把右侧的果汁向下推了50厘米——总共，我把果汁柱垂直移动了大约100厘米，也就是一米（39英寸）。当然，我们用呼吸管呼吸时是吸入空气，而不是呼出空气。所以也许吸入空气更容易？于是，我又做了一次实验，但这次我尽可能地把果汁吸到管子的最深处。然而，结果大致相同；果汁只在我吸的那一侧上升了大约50厘米——因此，它在另一侧下降了50厘米，而我已经筋疲力尽了。
I lean over, exhale completely, inhale to fill my lungs, take the right end of the tube in my mouth, and blow into it as hard as I can. My cheeks sink in, my eyes bug out, and the juice inches up in the left side of the U tube, and just barely rises by—could you guess?—50 centimeters. It takes everything I have to get it there, and I can’t hold it for more than a few seconds. So, I have pushed the juice up 50 centimeters on the left side, which means that I have also pushed it down 50 centimeters on the right side—in total, I have displaced the column of juice about 100 centimeters vertically, or one full meter (39 inches). Of course we are sucking air in when we breathe through a snorkel, not blowing it out. So perhaps it’s easier to suck the air in? So, I do the experiment again, but this time I suck in the juice as far up the tube as I can. The result, however, is roughly the same; it only rises about 50 centimeters on the side that I suck—thus it goes down 50 centimeters on the other side, and I am utterly exhausted.
我刚才模拟了在水下1米处浮潜，相当于十分之一大气压。我的学生们总是对我的演示感到惊讶，他们觉得自己肯定比我这个老教授做得更好。于是我邀请一位身材魁梧的壮汉上来试试，他使出浑身解数后，脸涨得通红，一脸震惊。他只比我多潜了几厘米而已。
I have just imitated snorkeling 1 meter under water, the equivalent of one-tenth of an atmosphere. My students are invariably surprised by the demonstration, and they figure they can do better than their aging professor. So I invite a big strong guy to come up and give it a try, and after his best effort, his face is bright red, and he’s shocked. He’s only been able to do a little bit better—a couple of centimeters more—than I could.
事实证明，这几乎就是我们能用呼吸管下潜到的极限深度了——区区1米（约3英尺）。而且我们只能坚持几秒钟。这就是为什么大多数呼吸管都远短于1米，通常只有大约1英尺长的原因。不妨试试用任何类型的软管自制一根更长的呼吸管，看看会发生什么。
This, it turns out, is just about the upper limit of how far down we can go and still breathe through a snorkel—1 lousy meter (about 3 feet). And we could really only manage this for a few seconds. That’s why most snorkels are much shorter than 1 meter, usually only about a foot long. Try making yourself a longer snorkel—you can do so with any kind of tubing—and see what happens.
你可能想知道，当你潜入水中浮潜时，胸部究竟会承受多大的力。在水下1米处，静水压力约为十分之一大气压，或者说每平方厘米0.1千克。胸部的表面积大约为1平方英尺，约1000平方厘米。因此，作用在胸部的力约为1100千克，而肺部气压作用在胸腔内壁上的力也约为1000千克。所以，十分之一的压力差会转化为100千克的力差——相当于200磅的重量！从这个角度来看，浮潜是不是感觉难多了？如果你潜到10米深，静水压力会更大。压力将达到 1 个大气压，即每平方厘米表面积 1 公斤，作用在你可怜的胸部的力将比肺部 1 个大气压产生的向外力高出约 1000 公斤（1 吨）。
You may wonder just how much force is exerted on your chest when you submerge to do a little snorkeling. At 1 meter below the surface, the hydrostatic pressure amounts to about one-tenth of an atmosphere, or we could say one-tenth of a kilogram per square centimeter. Now the surface area of your chest is roughly one square foot, about 1,000 square centimeters. Thus the force on your chest is about 1,100 kilograms, and the force on the inner wall of your chest due to the air pressure in your lungs is about 1,000 kilograms. Therefore the one-tenth of pressure difference translates into a difference in force of 100 kilograms—a 200-pound weight! When you look at it from this perspective, snorkeling looks a lot harder, right? And if you went down 10 meters, the hydrostatic pressure would be 1 full atmosphere, 1 kilogram per square centimeter of surface, and the force on your poor chest would be about 1,000 kilograms (1 ton) higher than the outward force produced by the 1-atmosphere pressure in your lungs.
这就是为什么亚洲采珠人——其中一些人经常潜到30米深的海底——要冒着生命危险在如此深的海底作业的原因。由于他们无法使用呼吸管，只能屏住呼吸，而他们只能屏住呼吸几分钟，所以他们必须动作迅速。
This is why Asian pearl divers—some of whom routinely dove down 30 meters—risked their lives at such depths. Because they could not snorkel, they had to hold their breath, which they could do only for a few minutes, so they had to be quick about their work.
只有现在你才能真正体会到潜艇所代表的工程成就。我们来设想一下，一艘潜艇潜入水下10米，假设艇内气压为1个大气压。艇内静水压力（即潜艇内外压力差）约为每平方米10000公斤，约合每平方米10吨。由此可见，即使是非常小的潜艇，也必须非常坚固才能下潜到10米深。
Only now can you really appreciate the engineering achievement represented by a submarine. Let’s think about a submarine at 10 meters down and assume that the air pressure inside is 1 atmosphere. The hydrostatic pressure (which is the pressure difference between outside and inside the sub) is about 10,000 kilograms per square meter, about 10 tons per square meter, so you can see that even a very small submarine has to be very strong to dive only 10 meters.
正是这一点，使得十七世纪初发明潜艇的科内利斯·范·德雷贝尔（Cornelis van Drebbel，值得庆幸的是，他是荷兰人）的成就如此令人惊叹。他只能在水下约5米处操控潜艇，即便如此，他仍然要应对半个大气压的静水压力，而且他竟然是用皮革和木头制造的！当时的记载表明，他曾在英国泰晤士河上进行试验，成功地在这样的深度操控过一艘潜艇。据说这艘潜艇由六名桨手划桨驱动，可搭载十六名乘客，并能潜航数小时。浮筒将“通气管”托出水面。这位发明家希望以此打动詹姆斯一世国王，试图说服他为海军订购一批潜艇，但可惜的是，国王和他的海军将领们并未被充分打动，这艘潜艇最终也从未投入实战。作为秘密武器，范·德雷贝尔的潜艇或许并不出彩，但作为一项工程壮举，它绝对令人叹为观止。您可以在以下网站了解更多关于范·德雷贝尔和早期潜艇的信息：www.dutchsubmarines.com/specials/special_drebbel.htm。
This is what makes the accomplishment of the fellow who invented the submarine in the early seventeenth century—Cornelis van Drebbel, who was Dutch, I’m happy to say—so astonishing. He could only operate it about 5 meters below the surface of the water, but even so, he had to deal with a hydrostatic pressure of half an atmosphere, and he built it of leather and wood! Accounts from the time say that he successfully maneuvered one of his crafts at this depth in trials on the Thames River, in England. This model was said to be powered by six oarsmen, could carry sixteen passengers, and could stay submerged for several hours. Floats held the “snorkels” just above the surface of the water. The inventor was hoping to impress King James I, trying to entice him to order a number of the crafts for his navy, but alas, the king and his admirals were not sufficiently impressed, and the sub was never used in combat. As a secret weapon, perhaps, van Drebbel’s sub was underwhelming, but as a feat of engineering it was absolutely remarkable. You can find out more about Van Drebbel and early submarines at this website: www.dutch submarines.com/specials/special_drebbel.htm.
现代海军潜艇究竟能潜到多深的深度，这是一个军事问题。虽然具体深度仍属秘密，但普遍认为它们可以下潜到约1000米（3300英尺）的深度，那里的静水压力约为100个大气压，也就是每平方米100万公斤（1000吨）。不出所料，美国潜艇采用的是高强度钢材。据说俄罗斯潜艇的下潜深度更深，因为它们采用的是强度更高的钛合金。
Just how far down modern navy submarines can dive is a military secret, but the prevailing wisdom is that they can go about 1,000 meters (3300 feet) deep, where the hydrostatic pressure is around 100 atmospheres, a million kilos (1,000 tons) per square meter. Not surprisingly, U.S. subs are made of very high grade steel. Russian submarines are said to be able to go even deeper, because they’re made of stronger titanium.
要演示潜艇如果艇壁不够坚固或者下潜过深会发生什么，其实很简单。我把一个真空泵连接到一个一加仑大小的油漆罐上，慢慢地把罐里的空气抽出来。罐内外的气压差最多只能达到一个大气压（想想潜艇的深度！）。我们知道油漆罐通常很结实，但就在我们眼前，由于气压差的作用，它像一个脆弱的铝制汽水罐一样被挤压变形了。看起来就像一个看不见的巨人抓住它，用拳头狠狠地捏了一下。我们可能都曾经用塑料水瓶做过类似的事情，把里面的空气抽出来，让它变形。直觉上，你可能会认为瓶子变形是因为你用力吸气造成的。但真正的原因是，当我把油漆罐里的空气排空，或者你把水瓶里的空气吸出来一些时，外界气压就没有足够的压力来与之对抗。这就是我们自身大气压力随时可能产生的作用。绝对随时。
It’s easy to demonstrate what would happen to a submarine if its walls weren’t strong enough, or if it dove too deep. To do this I hook up a vacuum pump to a gallon-size paint can and slowly pump the air out of the can. The pressure difference between the air outside and inside can only be as high as 1 atmosphere (compare that with the submarine!). We know that paint cans are fairly strong, but right before our eyes, because of the pressure difference, this one crumples like a flimsy aluminum soda can. It appears as though an invisible giant has taken hold of it and squeezed it in its fist. We’ve probably all done essentially the same thing at some point with a plastic water bottle, sucking a good bit of the air out of it and making it crumple. Intuitively, you may think the bottle scrunches up because of the power with which you’ve sucked on the bottle. But the real reason is that when I empty the air from the paint can, or you suck some of the air out of the water bottle, the outside air pressure no longer has enough competing pressure to push back against it. That’s what the pressure of our own atmosphere is ready to do at any moment. Absolutely any moment.
一个金属油漆罐，一个塑料水瓶——这些都是再普通不过的东西，对吧？但如果我们用物理学家的视角来看待它们，就会发现截然不同的东西：一种极其强大的力的平衡。如果没有这些大多看不见的力的平衡——大气压力、静水压力以及不可阻挡的引力——我们的生活将无法存在。这些力如此强大，一旦它们哪怕稍微失去平衡，都可能引发灾难。试想一下，如果一架飞机在35000英尺（约10600米）的高空（那里的气压只有大约0.25个大气压）以每小时550英里（约880公里）的速度飞行时，机身接缝处出现泄漏会怎样？或者，如果巴尔的摩港隧道顶部，在帕塔普斯科河水面以下50到100英尺（约15到30米）处出现一条细小的裂缝会怎样？
A metal paint can, a plastic water bottle—these are totally mundane things, right? But if we look at them the way a physicist does, we see something entirely different: a balance of fantastically powerful forces. Our lives would not be possible without these balances of largely invisible forces, forces due to atmospheric and hydrostatic pressure, and the inexorable force of gravity. These forces are so powerful that if—or when—they get even a little bit out of equilibrium, they can cause catastrophe. Suppose a leak develops in the seam of an airplane fuselage at 35,000 feet (where the atmospheric pressure is only about 0.25 atmospheres) while the plane is traveling at 550 miles per hour? Or a hairline crack opens up in the roof of the Baltimore Harbor Tunnel, 50 feet to 100 feet below the surface of the Patapsco River?
下次你走在城市街道上时，不妨试着像物理学家一样思考。你真正看到的是什么？首先，你看到的是每栋建筑内部激烈搏斗的结果，而我指的并非办公室政治。在这场博弈的一侧，地球引力正试图将一切拉向地面——不仅是墙壁、地板和天花板，还包括办公桌、空调管道、邮件槽、电梯、秘书和首席执行官，甚至连早晨的咖啡和羊角面包也不放过。而在另一侧，钢铁、砖瓦、混凝土以及最终大地本身的力量，正将建筑向上推向天空。
The next time you walk down a city street, try thinking like a physicist. What are you really seeing? For one, you are seeing the result of a furious battle raging inside every single building, and I don’t mean office politics. On one side of the battlefield, the force of Earth’s gravitational attraction is striving to pull all of it down—not only the walls and floors and ceilings, but the desks, air-conditioning ducts, mail chutes, elevators, secretaries and CEOs alike, even the morning coffee and croissants. On the other side, the combined force of the steel and brick and concrete and ultimately the ground itself are pushing the building up into the sky.
因此，我们可以这样理解建筑和施工工程：它们是与向下的重力抗争直至其停止的艺术。我们或许会认为某些轻盈的摩天大楼摆脱了重力的束缚。其实不然——它们只是将这场抗争提升到了新的高度。仔细想想，你会发现这种僵局只是暂时的。建筑材料会腐蚀、老化和衰败，而自然界的力量却始终无情。这只是时间问题。
One way to think of architecture and construction engineering, then, is that they are the arts of battling the downward force to a standstill. We may think of certain feathery skyscrapers as having escaped gravity. They’ve done no such thing—they’ve taken the battle literally to new heights. If you think about it for a little while, you’ll see that the stalemate is only temporary. Building materials corrode, weaken, and decay, while the forces of our natural world are relentless. It’s only a matter of time.
这些微妙的平衡在大城市里可能最具威胁性。想想2007年发生在纽约市的一起可怕事故：一条埋在地下、直径两英尺、已有83年历史的管道突然无法承受其输送的高压蒸汽。由此产生的蒸汽喷涌而出，在莱克星顿大道上炸出一个20英尺的大洞，吞没了一辆拖车，其高度甚至超过了附近77层的克莱斯勒大厦。如果这种潜在的破坏性力量不能始终保持如此精妙的平衡，恐怕没有人会走在城市的街道上。
These balancing acts may be most threatening in big cities. Consider a horrible accident that happened in New York City in 2007, when an eighty-three-year-old 2-foot-wide pipe beneath the street suddenly could no longer contain the highly pressurized steam it carried. The resulting geyser blew a 20-foot hole in Lexington Avenue, engulfing a tow truck, and shot up higher than the nearby seventy-seven-story Chrysler Building. If such potentially destructive forces were not held in exquisite balance nearly all of the time, no one would walk any city streets.
这些强大力量之间的僵持局面并非完全是人类活动的结果。以树木为例。它们平静、沉默、静止、缓慢、默默无闻——它们运用数十种生物策略来对抗重力和静水压力。每年都能萌发新枝，不断在树干上增加年轮，使树木更加强壮，即使树木与地球之间的引力越来越强，这本身就是一项了不起的成就。而且，树木还能将树液输送到最高的枝干。树木能够长到10米以上，这难道不令人惊叹吗？毕竟，水只能向上流动。我的吸管里水位最高也就10米，再也上不去了；为什么（又是如何）树上的水能上升得那么高呢？最高的红杉树超过300英尺，它们似乎能把水一直输送到最顶端的叶子。
These stalemates between immensely powerful forces are not all the product of human handiwork. Consider trees. Calm, silent, immobile, slow, uncomplaining—they employ dozens of biological strategies to combat the force of gravity as well as hydrostatic pressure. What an achievement to sprout new branches every year, to continue putting new rings on its trunk, making the tree stronger even as the gravitational attraction between the tree and the earth grows more powerful. And still a tree pushes sap up into its very highest branches. Isn’t it amazing that trees can be taller than about 10 meters? After all, water can only rise 10 meters in my straw, never higher; why (and how) would water be able to rise much higher in trees? The tallest redwoods are more than 300 feet tall, and somehow they pull water all the way up to their topmost leaves.
这就是为什么我对暴风雨后折断的大树如此同情。狂风，或是枝头堆积的冰雪，破坏了大树原本维系的微妙平衡。想到这场永无止境的战斗，我更加感激远古时代，我们的祖先不再四肢着地，而是用两条腿站立，开始迎接挑战的那一天。
This is why I feel such sympathy for a great tree broken after a storm. Fierce winds, or ice and heavy snow accumulating on its branches, have managed to upset the delicate balance of forces the tree had been orchestrating. Thinking about this unending battle, I find myself appreciating all the more that ancient day when our ancestors stood on two legs rather than four and began to rise to the occasion.
伯努利及其超越
Bernoulli and Beyond
人类克服重力、驾驭气压变化的壮举，或许没有比飞行更令人叹为观止的了。它是如何实现的呢？你可能听说过，这与伯努利原理以及空气在机翼上下流动有关。这一原理以数学家丹尼尔·伯努利的名字命名，他于1738年在其著作《流体动力学》中发表了我们现在称之为伯努利方程的理论。简而言之，该原理指出，对于液体和气体流动，当流速增加时，流体中的压力会降低。这听起来可能有些难以理解，但你可以亲眼目睹这一现象。
There may be no more awe-inspiring human achievement in defying the incessant pull of gravity and mastering the shifting winds of air pressure than flight. How does it work? You may have heard that it has to do with Bernoulli’s principle and air flowing under and over the wings. This principle is named for the mathematician Daniel Bernoulli who published what we now call Bernoulli’s equation in his book Hydrodynamica in 1738. Simply put, the principle says that for liquid and gas flows, when the speed of a flow increases, the pressure in the flow decreases. That is hard to wrap your mind around, but you can see this in action.
拿一张普通的纸，比如一张 8.5 × 11 英寸的纸，举到嘴边（不要放进嘴里），短边朝向嘴边。由于重力作用，纸会向下卷曲。现在用力朝纸的顶部吹气，观察会发生什么。你会看到纸向上弹起。根据吹气的力度，你可以让纸跳得更高。你刚刚演示了伯努利原理，这个简单的现象也有助于解释飞机是如何飞行的。虽然我们很多人可能已经习以为常，但亲眼目睹一架 747 起飞，或者被安全带固定在座位上，看着它升空，仍然是一种非常奇特的体验。看看孩子们第一次看到飞机起飞时的兴奋表情就知道了。一架波音 747-8 的最大起飞重量接近一百万磅。它究竟是如何保持飞行的呢？
Hold a single sheet of paper, say an 8.5 × 11–inch standard sheet, up to your mouth (not in your mouth) with the short edge at your mouth. The paper will curl down because of gravity. Now blow hard straight out across the top of the paper, and watch what happens. You’ll see the paper rise. And depending on how hard you blow, you can make the paper really jump up. You’ve just demonstrated Bernoulli’s principle, and this simple phenomenon also helps explain how airplanes fly. Though many of us may have become used to the sight, watching a 747 take off, or being strapped in a seat when the thing lifts off, is a truly strange experience. Just watch the delight with which little children see their first plane take off. A Boeing 747-8 has a maximum takeoff weight of nearly a million pounds. How on earth does it stay aloft?
飞机机翼的设计使得其上方的气流速度相对于下方的气流速度更快。由于伯努利原理，机翼上方的高速气流会降低机翼上方的气压，而由此产生的低压与机翼下方的高压之间的压差就形成了向上的升力。我们称之为伯努利升力。许多物理书籍都认为伯努利升力是飞机上升升力的唯一原因——事实上，这种说法非常普遍。然而，只要稍加思考，你就会发现这种说法并不成立。因为如果伯努利升力真的存在，飞机又怎么可能倒飞呢？
An airplane wing is designed so that the air that passes above it speeds up relative to the air that passes underneath it. Because of Bernoulli, the faster airflow on top of the wing lowers the air pressure above the wing, and the resulting difference between that low pressure and the higher pressure under the wing provides upward lift. Let’s call this Bernoulli lift. Many physics books tell you that Bernoulli lift is entirely responsible for the upward lift of airplanes—in fact, this idea is all over the place. And yet, if you think about it for a minute or two, you can figure out that it cannot be true. Because if it were true, how would planes ever fly upside down?
因此，很明显，伯努利原理本身并不能完全解释升力。除了伯努利升力之外，还有所谓的反作用升力。BC Johnson 在他精彩的文章《空气动力升力、伯努利效应、反作用升力》（http://mb-soft.com/public2/lift.html）中对此进行了详细描述。反作用升力（得名于牛顿第三定律：作用力与反作用力大小相等、方向相反）产生于空气流经向上倾斜的机翼下方时。这股从机翼前缘流向后缘的空气受到机翼的向下推力。这就是“作用力”。这个作用力必然会受到大小相等、向上推力的反作用，因此机翼上才会产生升力。以波音747为例（以550英里/小时的速度在约30,000英尺的高度巡航），超过80%的升力来自反作用升力，而来自伯努利升力的升力不到20%。
So it’s obvious that Bernoulli’s principle alone cannot be the sole reason for the upward lift. In addition to the Bernoulli lift there is a so-called reaction lift. B. C. Johnson describes this in detail in his delightful article “Aerodynamic Lift, Bernoulli Effect, Reaction Lift” (http://mb-soft.com/public2/lift.html). Reaction lift (named for Newton’s third law: for every action there is an equal and opposite reaction) comes about when air passes underneath an airplane wing angled upward. That air, moving from the front of the wing to the back, is pushed downward by the wing. That’s the “action.” That action must be met by an equal reaction of air pushing upward, so there is upward lift on the wing. In the case of a Boeing 747 (cruising at 550 miles per hour at an altitude of about 30,000 feet) more than 80 percent of the lift comes from reaction lift, and less than 20 percent from Bernoulli lift.
下次你坐车的时候，可以很轻松地自己演示一下反作用力抬升。事实上，你小时候可能就做过这个动作。当车子行驶时，摇下车窗，把胳膊伸出车外，手掌朝向车子行驶的方向，然后调整手掌的角度，使手指向上。你会感觉到手掌被向上推了一下。瞧！这就是反作用力抬升。
You can demonstrate reaction lift pretty easily yourself the next time you travel in a car. In fact, you may even have done this when you were little. When the car is moving, roll down the window, stick your arm outside, hold your hand in the direction that the car is moving, and tilt the angle of your hand such that your fingers are pointing upward. You will feel your hand pushed upward. Voila! Reaction lift.
你现在可能认为自己明白了为什么有些飞机可以倒飞。但是，你是否意识到，如果飞机翻滚180度，伯努利力和反作用力都会指向下方？记住，在正常飞行中，反作用力向上是因为机翼向上倾斜，但翻滚 180 度后，机翼会向下倾斜。
You may think now that you understand why some planes can fly upside down. However, do you realize that if a plane rolls over 180 degrees that both the Bernoulli force and the reaction force will now be pointing downward? Remember, in normal flight the reaction force is upward because the wings are angled upward, but after a 180-degree rollover, they will be angled downward.
再次进行实验，感受手上的反作用力。只要手指向上倾斜，你就会感觉到向上的力。现在改变角度，使手指向下倾斜；此时你会感觉到向下的力。
Do the experiment again to feel the reaction lift on your hand. As long as you tilt your fingers upward you will feel an upward force. Now change the angle such that your fingers are tilted downward; you will now feel a force in the downward direction.
那么，为什么飞机可以倒飞呢？所需的升力必然来自向上的反作用力，因为这是唯一的动力来源。如果飞行员（倒飞时）将机头抬升到足够高，使机翼再次向上倾斜，就能实现倒飞。这非常棘手，只有经验极其丰富的飞行员才能做到。仅仅依靠反作用升力也相当危险，因为反作用升力本身就不稳定。你可以把手伸出车窗外做个实验，就能感受到这种不稳定性。你的手会剧烈晃动。事实上，正是由于难以控制反作用升力，才导致大多数飞机失事发生在起飞和着陆阶段。起飞和着陆时，反作用升力所占的升力比例高于正常飞行阶段。这就是为什么大型客机着陆时，有时你会感觉到飞机摇晃的原因。
Why then is it possible to fly upside down? The required lift must somehow come from an upward reaction force, since that’s the only game in town. This becomes possible if the pilot (flying upside down) raises the front end of the plane enough so that the wings become angled upward again. This is a tricky business and only very experienced pilots can do it. It’s also rather dangerous to rely solely on reaction lift, since by nature reaction lift is not very stable. You can sense this instability doing the experiment with your hand outside the car window. Your hand jiggles around quite a bit. In fact, it’s this difficulty in controlling reaction lift that accounts for why most airplane crashes occur close to takeoff and landing. The fraction of lift accounted for by reaction lift is higher at takeoff and landing than during flight at normal altitude. This is why when a big airliner lands, you can sometimes feel the plane wobble.
偷酒贼
The Drink Thief
压力的奥秘的确令人费解，几乎无穷无尽。例如，想想用吸管喝东西的物理原理。这里还有一个谜题值得思考，一个绝妙的脑筋急转弯。
The mysteries of pressure are in truth almost endlessly perplexing. Come back, for example, to the physics of drinking with a straw. Here is one last puzzle to consider, a wonderful brainteaser.
某个周末在家，我自言自语道：“我想知道，我能用多长的吸管喝果汁呢？”我们都见过超长的吸管，通常弯弯曲曲的，孩子们很喜欢。
At home one weekend I said to myself, “I wonder what would be the longest straw that I could drink a glass of juice from.” We’ve all seen super-long straws, often with turns and twists in them, which children love.
我们之前看到，我们吸吮的力度最多只能将果汁吹到大约1米远——而且只能持续几秒钟——这意味着我用吸管吸果汁的高度不会超过1米（约3英尺）。所以我决定给自己剪一小段细长的吸管。我拿了一根一米长的塑料管试试看。没问题，我能轻松地把果汁吸上来。于是我决定剪一根三米长的——差不多十英尺——然后我爬上厨房的椅子，在地上放了一桶水，果然，我也能把水吸上来。太神奇了！然后我心想，如果我站在二楼，往下看，比如说有人在露台上喝着一大杯果汁、葡萄酒或其他什么——比如说一大杯蔓越莓伏特加——如果我有一根很长的吸管，能不能把他的饮料吸上来呢？我决定试一试，这便成了我最喜欢在课堂上做的演示之一。它总是能让学生们惊叹不已。
We saw earlier that we can only suck hard enough to displace juice about a maximum of 1 meter—and that only for a few seconds—meaning that I would not be able to suck up juice with a straw any higher than 1 meter (about 3 feet). So I decided to cut myself a piece of thin plastic tube 1 meter long and see if that would work. No problem; I could suck the juice up just fine. So I decided to cut a piece 3 meters long—that’s almost 10 feet—and I got up on a chair in my kitchen and put a bucket of water on the floor, and sure enough, I could suck it up that far too. Amazing. Then I thought to myself, if I were up on the second story of my house and I looked down at someone below, say out on a deck having a great big tumbler of juice, wine, or whatever—let’s say a very large cranberry and vodka—could I steal that drink by sucking it up if I had a really long straw? I decided to find out, and this led to one of the demonstrations I love to do in class. It never ceases to amaze the students.
我拿出一长串盘绕的透明塑料管，然后请前排一位学生自愿帮忙。我把一大杯蔓越莓汁——没有伏特加——放在教室地板上，让所有学生都能看到。我拿着塑料管，开始爬上一个高高的梯子；梯子离地面大约有16英尺——将近5米！
I pull out a long length of coiled-up clear plastic tubing and I ask for a front-row volunteer. I place a large glass beaker of cranberry juice—no vodka—on the floor in the classroom for all students to see. Holding the tubing, I begin to climb a tall ladder; it reaches about 16 feet off the floor—almost 5 meters!
“好了，这是我的吸管，”我说着，把吸管的一端递给学生。她把吸管的一端伸进烧杯里，我能感觉到学生们的期待。全班同学都难以置信我竟然能做到。要知道，他们亲眼目睹过我只能把蔓越莓汁吹出大约1米，也就是3英尺远。而现在我却离地大约16英尺高。我怎么可能做到呢？
“Okay, here’s my straw,” I say, dropping one end of the tubing to the student. She holds the end in the beaker, and I can feel the students’ anticipation. The class can’t quite believe I’m up there. Remember, they were witnesses to the fact that I could only displace the cranberry juice about 1 meter, or about 3 feet. Now I’m about 16 feet off the ground. How could I possibly do it?
我开始吸吮，随着果汁在管子里缓缓上升，我不禁发出几声低吟：先是1米，然后2米，接着是3米。之后液面略微下降，但很快果汁又开始缓慢上升，直到到达我的嘴边。我大声地“嗯”了一声，全班同学顿时爆发出热烈的掌声。这是怎么回事？为什么我能把果汁吸到这么高？
I begin sucking, grunting a bit as the juice rises slowly inside the tube: first 1 meter, then 2, and then 3. Then the level dips a little, but soon the juice resumes climbing very slowly again until it reaches my mouth. I say a loud “Mmmmm” and the class erupts in applause. What has been going on here? Why could I suck the juice up so high?
坦白说，我作弊了。不过这也没什么关系，因为这游戏本来就没有规则。每次吸完，吸不进去空气的时候，我就用舌头堵住管子的末端。换句话说，我把管子堵住了，就像我们之前看到的，这样就能把果汁留在管子里。然后我呼气，再开始吸，如此反复多次。我的嘴就像一个吸气泵，我的舌头就像一个止回阀。
Frankly, I cheat. Not that it matters, since there are no rules in the game. Every time after sucking, when I can’t take any more air in, I put my tongue over the end of the tube. In other words I close the tube off, and as we saw earlier, this will keep the juice up in the tube. I then exhale and I start sucking again, and repeat that scenario many times. My mouth becomes a kind of suction pump and my tongue a kind of stop valve.
为了让蔓越莓汁上升到16英尺高，我必须把管子里的气压降到大约半个大气压。对了，如果你好奇的话，我也可以对压力计用同样的方法，那样就能吸起更长的蔓越莓汁了。这是否意味着我也可以潜到湖面或海面下更深的地方呢？
To make the juice rise those 16 feet, I have to lower the pressure of the air in the tube to about half an atmosphere. And yes, if you’re wondering, I could have used the same trick with the manometer, and I would have been able to suck up a much longer column of cranberry juice. Does that mean that I could also snorkel much farther down beneath the surface of a lake or the sea?
你觉得呢？如果你知道答案，请告诉我！
What do you think? If you know the answer, drop me a note!
第五章
CHAPTER 5
上与下——外与内——彩虹
Over and Under—Outside and Inside—the Rainbow
日常生活中许多细微的美好——它们有时真的令人惊叹——却常常被我们忽略，因为我们没有接受过如何发现它们的训练。我记得四五年前的一个早晨，我坐在我最喜欢的红蓝相间的里特维尔德椅上喝着浓缩咖啡，突然注意到墙上出现了一串美丽的圆形光点，它们与窗外树叶投下的斑驳光影交相辉映。我欣喜若狂，眼睛都亮了起来。我不太确定发生了什么，但我的妻子苏珊一如既往地敏锐，她觉得是不是有什么不对劲。
So many of the little wonders of the everyday world—which can be truly spectacular—go unobserved most of the time because we haven’t been trained how to see them. I remember one morning, four or five years ago, when I was drinking my morning espresso in my favorite red and blue Rietveld chair, and suddenly I noticed this beautiful pattern of round spots of light on the wall, amidst the flickering of shadows thrown by the leaves of a tree outside the window. I was so delighted to have spotted them that my eyes lit up. Not sure what had happened, but with her usual astuteness, my wife, Susan, wondered if something was the matter.
“你知道那是什么吗？”我指着那些光圈问道，“你明白这是怎么回事吗？”然后我解释道。你可能会觉得光线会在墙上形成许多细小的光点，而不是光圈，对吧？但叶片间的许多小孔就像暗箱或针孔相机一样，会重现光源——在这个例子中是太阳——的影像。无论光线穿过的孔洞形状如何，都会形成光圈。只要开口较小，光线就会流动，投射到墙上的就是光源本身的形状。
“Do you know what that is?” I responded, pointing to the light circles. “Do you understand why that’s happening?” Then I explained. You might expect the light to make lots of little shimmerings on the wall rather than circles, right? But each of the many small openings between the leaves was acting like a camera obscura, a pinhole camera, and such a camera reproduces the image of the light source—in this case the Sun. No matter what the shapes of the openings through which the light is streaming, as long as the opening is small, it’s the shape of the light source itself that’s re-created on the wall.
所以，在日偏食期间，透过窗户照射进来的阳光不会再在墙上留下圆形的光斑——所有的圆形都会被切掉一部分，因为那正是太阳的形状。亚里士多德两千多年前就明白这一点了！亲眼看到卧室墙上那些光点，真是太神奇了，它们展现了光的奇妙特性。
So during a partial solar eclipse, sunlight pouring through my window wouldn’t make circles on my wall anymore—all the circles would have a bite taken out of them, because that would be the shape of the Sun. Aristotle knew this more than two thousand years ago! It was fantastic to see those light spots, right there on my bedroom wall, demonstrating the remarkable properties of light.
彩虹的秘密
Secrets of the Rainbow
事实上，光物理学的奇妙效应无处不在，有时体现在最平凡的景象中，有时则体现在大自然最美丽的造物中。以彩虹为例：它们是奇妙无比的自然现象，而且随处可见。伟大的科学家——例如被誉为光学之父的十一世纪穆斯林科学家兼数学家伊本·海赛姆、法国哲学家、数学家兼物理学家勒内·笛卡尔，以及艾萨克·牛顿爵士本人——都为之着迷，并试图解释它们的成因。然而，大多数物理老师在课堂上却对彩虹视而不见。我简直无法相信，事实上，我认为这简直是犯罪。
In truth, the marvelous effects of the physics of light are everywhere we look, sometimes in the most ordinary sights, and at other times in some of nature’s most beautiful creations. Take rainbows, for example: fantastic, wonderful phenomena. And they’re everywhere. Great scientists—Ibn al-Haytham, the eleventh-century Muslim scientist and mathematician known as the father of optics, the French philosopher, mathematician, and physicist René Descartes; and Sir Isaac Newton himself—found them captivating and tried to explain them. Yet most physics teachers ignore rainbows in their classes. I can’t believe this; in fact, I think it’s criminal.
彩虹的物理原理并不简单。但那又怎样呢？我们怎能拒绝探索如此激发我们想象力的事物？我们怎能不想了解这些壮丽造物背后那份内在之美的奥秘？我一直很喜欢讲授彩虹，我常告诉我的学生：“这堂课结束后，你们的人生将会彻底改变，永远不会。” 这对你们来说也是如此。
Not that the physics of rainbows is simple. But so what? How can we refuse to tackle something that pulls so powerfully on our imaginations? How can we not want to understand the mystery behind the intrinsic beauty of these glorious creations? I have always loved lecturing about them, and I tell my students, “At the end of this lecture, your life will never be the same again, never.” The same goes for you.
几十年来，我的学生和其他在网上观看过我讲座的人一直通过邮件和电子邮件给我发送彩虹和其他大气现象的精彩照片。我觉得自己仿佛拥有一个遍布全球的彩虹侦察队。其中一些照片非常精彩——尤其是尼亚加拉大瀑布的照片，那里有太多令人惊叹的彩虹。喷漆说这些蝴蝶结太漂亮了。也许你也想给我发些照片。请随意！
Former students and others who’ve watched my lectures on the web have been mailing and emailing me wonderful images of rainbows and other atmospheric phenomena for decades. I feel as though I have a network of rainbow scouts spread across the world. Some of these shots are extraordinary—especially those from Niagara Falls, which has so much spray that the bows are spectacular. Maybe you will want to send me pictures too. Feel free!
我相信你一生中至少见过几十次，甚至上百次彩虹。如果你在佛罗里达、夏威夷或其他阳光明媚但又经常下雨的热带地区待过，你看到的彩虹肯定更多。如果你在阳光灿烂的时候用软管或洒水器给花园浇水，你很可能也创造了彩虹。
I’m sure you’ve seen at least dozens, if not hundreds, of rainbows in your life. If you’ve spent time in Florida or Hawaii, or other tropical locations where there are frequent rain showers while the Sun shines, you’ve seen even more. If you’ve watered your garden with a hose or sprinkler when the Sun is shining, you’ve probably created rainbows.
我们大多数人都见过彩虹，但真正见过彩虹的人却寥寥无几。古代神话称彩虹为神之弓、连接凡人居所与神灵的桥梁或道路。在西方，彩虹最广为人知的象征意义是，在希伯来圣经中，彩虹代表着上帝不再降下毁灭大地的洪水：“我将我的彩虹置于云端。”
Most of us have looked at many rainbows, yet very few of us have ever seen rainbows. Ancient mythologies have called them gods’ bows, bridges or paths between the homes of mortals and the gods. Most famously in the West, the rainbow represented God’s promise in the Hebrew Bible never again to bring an all-destroying flood to the earth: “I do set my bow in the clouds.”
彩虹的魅力之一在于它们如此广阔，雄伟壮丽地横跨整个天空，却又如此短暂。但是，正如物理学中经常出现的情况一样，它们的起源在于数量极其庞大的极其微小的东西：漂浮在空中的微小水球，有时直径甚至不到1毫米（1/25英寸）。
Part of the charm of rainbows is that they are so expansive, spreading majestically, and so ephemerally, across the entire sky. But, as is so often true in physics, their origins lie in extraordinarily large numbers of something exceptionally minute: tiny spherical balls of water, sometimes less than 1 millimeter (1/25 of an inch) across, floating in the sky.
虽然科学家们至少一千年来一直在试图解释彩虹的起源，但艾萨克·牛顿在其1704年出版的《光学》一书中提出了第一个真正令人信服的解释。牛顿同时理解了几个对彩虹的形成至关重要的方面。首先，他证明了普通的白光是由所有颜色组成的（我原本想说“彩虹的所有颜色”，但这有点超前了）。他通过玻璃棱镜折射（弯曲）光线，将其分解成组成它的各种颜色。然后，他让折射后的光线再次通过另一个棱镜，将这些彩色光重新组合成白光，从而证明棱镜本身并没有以某种方式产生这些颜色。他还发现许多不同的物质都能折射光线，包括水。正是通过这些发现，他最终理解到雨滴对光线的折射和反射是形成彩虹的关键。
While scientists have been trying to explain the origins of rainbows for at least a millennium, it was Isaac Newton who offered the first truly convincing explanation in his 1704 work Opticks. Newton understood several things at once, all of which are essential for producing rainbows. First, he demonstrated that normal white light was composed of all the colors (I was going to say of “all the colors of the rainbow,” but that would be getting ahead of ourselves). By refracting (bending) light through a glass prism, he separated it into its component colors. Then, by sending the refracted light back through another prism, he combined the colored light back into white light, proving that the prism itself wasn’t creating the colors in some way. He also figured out that many different materials could refract light, including water. And this is how he came to understand that raindrops refracting and reflecting light were the key to producing a rainbow.
牛顿正确地得出结论：天空中的彩虹是太阳、无数雨滴和你的眼睛共同作用的成果，而你的眼睛必须以恰当的角度观察这些雨滴。为了理解彩虹的形成过程，我们需要深入了解光线进入雨滴时发生的情况。但请记住，我接下来要描述的这颗雨滴，实际上也适用于构成彩虹的无数雨滴。
A rainbow in the sky, Newton concluded correctly, is a successful collaboration between the Sun, zillions of raindrops, and your eyes, which must be observing those raindrops at just the right angles. In order to understand just how a rainbow is produced, we need to zero in on what happens when light enters a raindrop. But remember, everything I’m going to say about this single raindrop in reality applies to the countless drops that make up the rainbow.
要想看到彩虹，需要满足三个条件。首先，太阳必须在你身后。其次，你前方的天空必须有雨滴——这可能远在数英里之外，也可能只有几百码远。第三，阳光必须能够毫无阻碍地照射到雨滴上，例如没有云层遮挡。
For you to see a rainbow, three conditions need to be met. First, the Sun needs to be behind you. Second, there must be raindrops in the sky in front of you—this could be miles or just a few hundred yards away. Third, the sunlight must be able to reach the raindrops without any obstruction, such as clouds.
当一束光线进入雨滴并发生折射时，它会分解成组成它的所有颜色。红光的折射程度最小，而紫光的折射程度最大。所有这些不同颜色的光线都会继续向雨滴的后方传播。一部分光线会继续传播并射出雨滴，而另一部分光线则会以一定角度反射回雨滴的前方。事实上，有些光线会多次反射，但这在后面才会变得重要。目前，我们只关注只反射一次的光线。当光线从雨滴的前方射出时，一部分光线会再次发生折射，进一步分解成不同颜色的光线。
When a ray of light enters a raindrop and refracts, it separates into all of its component colors. Red light refracts, or bends, the least, while violet light refracts the most. All of these different-colored rays continue traveling toward the back of the raindrop. Some of the light keeps going and exits the raindrop, but some of it bounces back, or reflects, at an angle, toward the front of the raindrop. In fact, some of the light reflects more than once, but that only becomes important later. For the time being, we are only interested in the light that reflects just once. When the light exits the front of the drop, some of the light again refracts, separating the different colored rays still further.
阳光穿过雨滴后，经过多次折射、反射和再次折射，最终几乎完全改变了方向。我们之所以能看到彩虹，关键在于红光从雨滴射出的角度始终小于入射光的初始方向约42度。所有雨滴的情况都相同，因为太阳实际上距离我们无限远。红光射出的角度介于0度到42度之间，但绝不会超过42度，而且不同颜色的光的最大射出角度也各不相同。例如，紫光的最大射出角度约为40度。正是由于每种颜色的光射出角度不同，才形成了彩虹的条纹。
After these rays of sunlight refract, reflect, and refract again on their way out of the raindrop, they have pretty much reversed direction. Key to why we see rainbows is that red light exits the raindrop at angles that are always smaller than about 42 degrees from the original direction of the sunlight entering the drop. And this is the same for all raindrops, because the Sun for all practical purposes is infinitely far away. The angle at which the red light exits can be anything between 0 degrees and 42 degrees but never more than 42 degrees, and this maximum angle is different for each of the different colors. For violet light, the maximum angle is about 40 degrees. These different maximum angles for each color account for the stripes of colors in the rainbow.
在合适的条件下，有一种简单的方法可以观测到彩虹。如下图所示，如果我从太阳出发，穿过我的头顶，画一条线到地面上我影子的末端，这条线恰好与太阳指向雨滴的方向平行。太阳在天空中的位置越高，这条线就越陡峭，我的影子就越短。反之亦然。我们将这条从太阳出发，穿过我的头顶，到地面上我头顶影子的线称为假想线。这条线非常重要，因为它能告诉你应该在天空的哪个位置才能看到彩虹。
There is an easy way to spot a rainbow when conditions are right. As seen in the following figure, if I trace a line from the Sun through my head to the far end of my shadow on the ground, that line is precisely parallel to the direction from the Sun to the raindrops. The higher the Sun in the sky, the steeper this line will be, and the shorter my shadow. The converse is also the case. This line, from the Sun, through my head, to the shadow of my head on the ground, we will call the imaginary line. This line is very important as it will tell you where in the sky you should look to see the rainbow.
与“假想线”成 42 度角的雨滴均为红色；成 40 度角的雨滴为蓝色；角度小于 40 度的雨滴为白色（如同阳光）；角度大于 42 度的雨滴则不会发光（详见正文）。
All raindrops at 42 degrees from the “imaginary line” will be red. Those at 40 degrees will be blue. raindrops at angles smaller than 40 degrees will be white (like the sunlight). We will see no light from drops at angles larger than 42 degrees (see text).
如果你从那条假想线向外看大约42度——无论是正上方、正右还是正左——你就能看到彩虹的红色部分。从它向外看大约40度——无论是正上方、正右还是正左——你就能看到彩虹的紫色部分。但事实上，紫色在彩虹中很难被看到，所以蓝色更容易被看到。因此，我们以后就直接说蓝色吧。这些角度不就是我之前提到的光线离开雨滴时的最大角度吗？是的，这绝非巧合。再看看图。
If you look about 42 degrees away from that imaginary line—it doesn’t matter whether it’s straight up, to the right, or to the left—that’s where you will see the red band of the rainbow. At about 40 degrees away from it—up, right, or left—you will see the violet band of the rainbow. But the truth is that violet is hard to see in a rainbow, so you’ll see the blue much more easily. Therefore we’ll just say blue from now on. Aren’t these the same angles I mentioned earlier, talking about the maximum angles of the light leaving the raindrop? Yes, and it’s no accident. Look again at the figure.
彩虹中的蓝光带是怎么回事呢？记住，它的神奇数字大约是40度，比红光带小2度。因此，蓝光可以在40度角内折射、反射，并从不同的雨滴中折射出来。所以我们看到的蓝光位于距离假想线40度的位置。由于40度带比42度带更靠近假想线，蓝光带总是位于彩虹红光带的内侧。组成彩虹的其他颜色——橙色、黄色、绿色——则位于红光带和蓝光带之间。想了解更多相关内容，可以观看我关于彩虹的在线讲座，网址是http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-22/。
What about the blue band in the rainbow? Well, remember its magic number is just about 40 degrees, 2 degrees less than the red band. So blue light can be found refracting, reflecting, and refracting out of different raindrops at a maximum angle of 40 degrees. Thus we see blue light 40 degrees away from the imaginary line. Since the 40-degree band is closer to the imaginary line than the 42-degree band, the blue band will always be on the inside of the red band of the rainbow. The other colors making up the bow—orange, yellow, green—are found between the red and blue bands. For more about this you can take a look at my lecture on rainbows online, at http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-22/.
你可能会想，在蓝光的最大入射角下，我们看到的真的只有蓝光吗？毕竟，红光也能在40度入射角下出现，因为它小于42度。如果你问了这个问题，那真是太好了——你问得非常精辟。答案是，在任何一种颜色的最大入射角下，这种颜色会主导所有其他颜色。但是，对于红色来说，因为它的入射角最大，所以它是唯一可见的颜色。
Now you might wonder, at the maximum angle for blue light, are we seeing only blue light? After all, red light can also emerge at 40 degrees, as it is smaller than 42 degrees. If you’ve asked this question, more power to you—it’s a very astute one. The answer is that at the maximum angle for any given color, that color dominates all other colors. With red, though, because its angle is the highest, it is the only color.
为什么彩虹是弧形而不是直线？让我们回到从你的双眼到头顶阴影的那条假想线，以及神奇的数字42度。当你从这条假想线向各个方向测量42度时，你就能描绘出一道彩虹弧线。但你知道，并非所有的彩虹都是完整的弧线——有些只是天空中的一小段。这种情况发生在天空中各个方向的雨滴数量不足，或者彩虹的某些部分被遮挡在云层的阴影中时。
Why is the rainbow a bow and not a straight line? Go back to that imaginary line from your eyes to the shadow of your head, and the magic number 42 degrees. When you measure 42 degrees—in all directions—away from the imaginary line, you are tracing an arc of color. But you know that not all rainbows are full arcs—some are just little pieces in the sky. That happens when there aren’t enough raindrops in all directions in the sky or when certain parts of the rainbow are in the shadow of obstructing clouds.
太阳、雨滴和你的眼睛之间还有另一个重要的相互作用，一旦你了解了这一点，你就会更明白为什么彩虹——无论是天然的还是人造的——会呈现出现在的样子。例如，为什么有些彩虹巨大无比，而有些却只是沿着地平线延伸？你有时在汹涌的海浪中、喷泉里、瀑布中，甚至是花园水管喷出的水柱中看到的彩虹又是怎么回事呢？
There’s another important aspect to this collaboration between the Sun, the raindrops, and your eyes, and once you see it, you’ll understand lots more about why rainbows—natural as well as artificial—are the way they are. For example, why are some rainbows enormous, while others just hug the horizon? And what accounts for the rainbows you sometimes see in pounding surf, or in fountains, waterfalls, or the spray of your garden hose?
让我们回到那条从你的眼睛延伸到你头部阴影的假想线。这条线从你身后的太阳开始，一直延伸到地面。然而，在你的想象中，你可以将这条线无限延长，甚至远远超过你头部的阴影。这条假想线非常有用，你可以想象它穿过一个圆的中心（称为反日点），彩虹就位于这个圆的圆周上。这个圆代表了如果没有地球表面的阻挡，彩虹应该形成的位置。根据太阳在天空中的高度，彩虹在地平线上的位置也会有所不同。当太阳很高时，彩虹可能只是刚刚出现在地平线上；而在傍晚日落前或清晨日出前后，当太阳位置较低，你的影子很长时，彩虹可能会非常巨大，甚至延伸到天空的一半高度。为什么是一半呢？因为它的最大仰角是 42 度，接近 45 度，也就是头顶正上方 90 度的一半。
Let’s go back to the imaginary line that runs from your eyes to the shadow of your head. This line starts at the Sun, behind you, and extends to the ground. However, in your mind, you can extend this line as far as you want, even much farther than the shadow of your head. This imaginary line is very useful, as you can imagine it going through the center (called the antisolar point) of a circle, on the circumference of which is the rainbow. This circle represents where the rainbow would form if the surface of Earth didn’t get in its way. Depending upon how high in the sky the Sun is, a rainbow will also be lower or higher above the horizon. When the Sun is very high, the rainbow may only just peek above the horizon, whereas late in the afternoon just before sunset, or early in the morning just around sunrise, when the Sun is low in the sky and when your shadow is long, then a rainbow may be enormous, reaching halfway up into the sky. Why halfway? Because the maximum angle it can be over the horizon is 42 degrees, or close to 45 degrees, which is half of the 90 degrees that would be right overhead.
那么，如何才能看到彩虹呢？首先，要相信你对彩虹何时出现的直觉。我们大多数人都有这种直觉：比如暴雨前阳光灿烂的时候，或者暴雨过后阳光正好的时候。又或者，下着小雨，阳光还能照射到雨滴的时候。
So how can you go rainbow hunting? First of all, trust your instincts about when a rainbow might form. Most of us tend to have a good intuitive sense of that: those times when the Sun is shining just before a rainstorm, or when it comes out right after one. Or when there’s a light shower and the sunlight can still reach the raindrops.
当你感觉雨季来临的时候，这样做：首先，背对太阳。然后找到你头部的阴影，并向任何方向偏离这条假想线约42度的方向看去。如果阳光充足，雨滴也足够多，那么雨季就会如约而至，你会看到一个色彩斑斓的雨滴。
When you feel one coming on, here’s what you do. First, turn your back to the Sun. Then locate the shadow of your head, and look about 42 degrees in any direction away from the imaginary line. If there’s enough sunlight, and if there are enough raindrops, the collaboration will work and you will see a colorful bow.
假设你完全看不到太阳——它被云层或建筑物遮挡住了，但它显然仍在闪耀。只要太阳和雨滴之间没有云层阻挡，你仍然应该能看到彩虹。傍晚时分，我坐在朝东的客厅里，即使看不到西边的太阳，也能看到彩虹。事实上，大多数时候你不需要借助假想线和42度角的技巧就能看到彩虹，但有一种情况下，同时注意这两者会带来很大的不同。我喜欢在马萨诸塞州海岸附近的普拉姆岛海滩上散步。傍晚时分，太阳在西边，大海在东边。如果海浪足够高，并且形成许多小水滴，这些水滴就像雨滴一样，你就能看到彩虹的两小段：一段在假想线左侧约42度角处，另一段在右侧约42度角处。这些彩虹转瞬即逝，所以提前知道在哪里寻找它们会很有帮助。由于总会有更多的海浪涌来，只要你足够耐心，就一定能成功。本章稍后会详细介绍。
Suppose you cannot see the Sun at all—it’s somehow hidden by clouds or buildings, but it’s clearly shining. As long as there are no clouds between the Sun and the raindrops, you still ought to be able to see a rainbow. I can see rainbows in the late afternoon from my living room facing east when I cannot see the Sun that is in the west. Indeed, most of the time you don’t need the imaginary line and the 42-degree trick to spot a rainbow, but there is one situation where paying attention to both can make a big difference. I love to walk on the beaches of Plum Island off the Massachusetts coast. Late in the afternoon the sun is in the west and the ocean is to the east. If the waves are high enough and if they make lots of small water drops, these droplets act like raindrops and you can see two small pieces of the rainbow: one piece at about 42 degrees to the left of the imaginary line and a second piece about 42 degrees to the right. These rainbows only last for a split second, so it’s a huge help in spotting them if you know where to look in advance. Since there are always more waves coming, you will always succeed if you can be patient enough. More about this later in this chapter.
下次看到彩虹时，不妨留意一下这个现象。还记得我们之前讨论过的，某些光线从雨滴中折射的最大角度吗？虽然你会看到某些雨滴呈现出蓝色、红色或绿色，但雨滴本身并不能如此挑剔：它们也会折射、反射和再次折射大量光线，折射角度小于40度。这些光线是由各种颜色以大致相等的强度混合而成的，我们看到的就是白光。这就是为什么在彩虹的蓝色区域内，天空会显得格外明亮洁白。与此同时，所有折射、反射和再次折射的光线都无法以超过42度的角度从雨滴中射出，因此彩虹外侧的天空比彩虹内侧的天空更暗。如果你比较彩虹两侧天空的亮度，这种现象会更加明显。如果你不特意去观察，可能根本不会注意到它。在大气光学网站www.atoptics.co.uk上，你可以看到一些非常漂亮的彩虹图片，从中可以看到这种效果。
Here is another thing you can try to look for, the next time you spot a rainbow. Remember our discussion of the maximum angle at which certain light can refract out of the raindrop? Well, even though you will see blue, or red, or green from certain raindrops, raindrops themselves cannot be so choosy: they refract, reflect, and refract lots of light at less than a 40-degree angle too. This light is a mixture of all the different colors at roughly equal intensities, which we see as white light. That’s why, inside the blue band of a rainbow, the sky is very bright and white. At the same time, none of the light that refracts, reflects, and refracts again can exit raindrops beyond the 42-degree angle, so the sky just outside the bow is darker than inside the bow. This effect is most visible if you compare the brightness of the sky on either side of the rainbow. If you’re not specifically looking for it, you probably won’t even notice it. There are excellent images of rainbows in which you can see this effect on the Atmospheric Optics website, at www.atoptics.co.uk.
当我开始向学生解释彩虹时，我才意识到……它们真是一个丰富的课题——而我还有很多东西需要学习。就拿双彩虹来说吧，你可能时不时会见到。事实上，天空中几乎总是有两道彩虹：一道是所谓的主彩虹，也就是我一直在讨论的那道，另一道是我们称之为副彩虹的那道。
Once I began explaining rainbows to my students, I realized just how rich a subject they are—and how much more I had to learn. Take double rainbows, which you’ve probably seen from time to time. In fact, there are almost always two rainbows in the sky: the so-called primary bow, the one I’ve been discussing, and what we call the secondary bow.
如果你见过双彩虹，你可能已经注意到，副虹比主虹暗淡得多。但你或许没有注意到，副虹的颜色顺序是外侧蓝色内侧红色，这与主虹的颜色顺序正好相反。本书的插图中有一张非常精彩的双彩虹照片。
If you’ve seen a double rainbow, you’ve probably noticed that the secondary bow is much fainter than the primary bow. You probably haven’t noticed, though, that the order of colors in the secondary bow is blue on the outside and red on the inside, the reverse of that in the primary. There is an excellent photograph of a double rainbow in this book’s photo insert.
为了理解次级彩虹的成因，我们必须回到理想的雨滴——当然，别忘了，实际上形成次级彩虹需要无数个雨滴。进入雨滴的光线有些只反射一次；有些则反射两次后才射出。虽然进入任何雨滴的光线都可以在雨滴内部多次反射，但主彩虹仅由反射一次的光线形成。而次级彩虹则仅由在雨滴内部反射两次后再折射射出的光线形成。正是由于在雨滴内部的这额外反射，次级彩虹的颜色才会反转。
In order to understand the origin of the secondary bow, we have to go back to our ideal raindrop—remember, of course, that it actually takes zillions of drops to make up a secondary rainbow as well. Some of the light rays entering the drops reflect just once; others reflect twice before exiting. While light rays entering any given raindrop can reflect many times inside it, the primary bow is only created by those that reflect once. The secondary bow, on the other hand, is created only by those that reflect twice inside before refracting on the way out. This extra bounce inside the raindrop is the reason the colors are reversed in the secondary bow.
次虹的位置与主虹不同——它总是位于主虹的外侧——这是因为两次反射的红色光线从雨滴射出的角度总是大于（没错，就是大于）大约50度，而两次反射的蓝色光线射出的角度总是大于大约53度。因此，你需要在主虹外侧大约10度的位置寻找次虹。次虹之所以暗淡得多，是因为雨滴内部两次反射的光线远少于一次反射的光线，所以形成虹的光线也更少。当然，这就是为什么次虹有时难以观测的原因。不过，既然你已经知道次虹通常伴随主虹出现，并且知道在哪里可以找到它们，我相信你以后会看到更多次虹。我还建议你花几分钟时间浏览一下大气光学网站。
The reason the secondary bow is in a different position from the primary bow—always outside it—is that twice-reflected red rays exit the drop at angles always larger (yes, larger) than about 50 degrees, and the twice-reflected blue rays come out at angles always larger than about 53 degrees. You therefore need to look for the secondary bow about 10 degrees outside the primary bow. The reason that the secondary bow is much fainter is that so much less light reflects inside the raindrops twice than reflects once, so there’s less light to make the bow. This is, of course, why it can be hard to see the secondary bow, but now that you know they often accompany primary rainbows, and where to look for them, I’m confident you’ll see lots more. I also suggest that you spend a few minutes on the Atmospheric Optics website.
既然你知道彩虹的成因，你就可以做一些小表演了。只需一根花园水管，你就能在自家后院、车道甚至人行道上创造光学奇观。但由于你可以操控雨滴，而且雨滴离你很近，所以自然界中存在一些显著差异。首先，即使太阳高悬空中，你也能制造出彩虹。为什么呢？因为你可以让雨滴落在你和地面上的影子之间，而这种情况在自然界中很少发生。只要有阳光能够照射到的雨滴，就能出现彩虹。你可能已经这样做过了，只是没有像现在这样有意识地去观察而已。
Now that you know what makes rainbows, you can perform a little optical magic in your own backyard or on your driveway or even on the sidewalk, with just a garden hose. But because you can manipulate the raindrops, and they are physically close to you, there are a couple of big differences. For one thing, you can make a rainbow even when the Sun is high in the sky. Why? Because you can make raindrops between you and your shadow on the ground, something that rarely happens naturally. As long as there are raindrops that the sunlight can reach, there can be rainbows. You may have done this already, but perhaps not as purposefully.
如果软管末端有喷嘴，请将其调至细雾模式，使水滴非常小。当太阳高悬空中时，将喷嘴指向地面开始喷洒。你无法一次性看到完整的彩虹，但你会看到彩虹的一部分。随着你继续以圆圈方式移动喷嘴，你会一块一块地看到完整的彩虹。为什么要这样做呢？因为你的后脑勺上没有眼睛！
If you have a nozzle on the end of the hose, adjust it to a fine spray, so the droplets are quite small, and when the Sun is high in the sky, point the nozzle toward the ground and start spraying. You cannot see the entire circle all at once, but you will see pieces of the rainbow. As you continue moving the nozzle in a circle, piece by piece you will see the entire circle of the rainbow. Why do you have to do it this way? Because you don’t have eyes in the back of your head!
你会看到与假想线成大约42度角的地方出现红色，圆弧的内缘会是蓝色，圆弧内部则会看到白光。我喜欢一边浇花一边进行这种小小的“创造”活动，尤其令人满足的是，我可以转身360度，创造出一个完整的彩虹。（当然，这样一来，太阳就不一定总在你身后了。）
You will see red at about 42 degrees from the imaginary line, the inside edge of the circular bow will be blue, and inside the bow you will see white light. I love performing this little act of creation while watering my garden, and it’s especially satisfying to be able to turn all the way around and make a complete 360-degree rainbow. (The Sun, of course, will then not always be behind you.)
1972年一个寒冷的冬日，为了给班上的学生拍到一些自制彩虹的好照片，我使出浑身解数，让当时只有七岁的女儿艾玛拿着水管在院子里往高处喷水，而我则忙着拍照。不过，我想，身为科学家的女儿，为了科学，总得受点苦吧。我的确拍到了一些很棒的照片；我甚至还拍到了第二道彩虹，以我家沥青车道为背景，与彩虹的颜色形成了鲜明的对比。你可以在插图中看到艾玛的照片。
One cold winter day in 1972 I was so determined to get some good photos of these homemade rainbows for my class that I made my poor daughter Emma, who was just seven, hold the hose in my yard, squirting the water high in the air, while I snapped away with the camera. But I guess when you’re the daughter of a scientist you have to suffer a little bit for the sake of science. And I did get some great pictures; I even managed to photograph the secondary bow, using my contrasting blacktop driveway as the background. You can see the picture of Emma in the insert.
我希望你能尝试一下这个实验——不过最好在夏天进行。如果你没看到第二道彩虹也不要太失望——如果你的车道不够暗，它可能太淡而看不见。
I hope you’ll try this experiment—but do it in the summer. And don’t be too disappointed if you don’t see the secondary bow—it may be too faint to show up if your driveway isn’t dark enough.
从现在开始，掌握了如何辨认彩虹的方法，你会发现自己越来越想去寻找它们。我常常忍不住。前几天，我和苏珊开车回家，开始下雨，但我们一路向西，迎着阳光。于是，尽管路上车很多，我还是把车停在了路边；我下车转身，就看到了它，真是太美了！
From now on, with this understanding of how to spot rainbows, you’ll find yourself compelled to look for them more and more. I often can’t help myself. The other day as Susan and I were driving home, it started to rain, but we were driving directly west, into the Sun. So I pulled over, even though there was a good deal of traffic; I got out of the car and turned around, and there it was, a real beauty!
我承认，每当阳光明媚的日子里路过喷泉，我都会特意找个合适的位置，希望能找到那道我知道一定会出现的彩虹。如果你在阳光灿烂的日子路过喷泉，不妨也试试。背对太阳，站在太阳和喷泉之间，记住喷泉的水柱就像悬浮在空中的雨滴。找到你头部的影子——这就是你想象中的直线。然后，将视线向这条直线偏转42度。如果那个方向有足够的雨滴，你就能看到彩虹的红色部分，然后彩虹的其余部分就会立刻映入眼帘。在喷泉中看到完整的半圆形彩虹并不常见——只有非常靠近喷泉才能看到——但那景象如此美丽，总是值得一试。
I confess that whenever I walk by a fountain when the sun is shining, I position myself so I can search for the rainbow I know will be there. If you’re passing by a fountain on a sunny day, give it a try. Stand between the Sun and the fountain with your back to the Sun, and remember that the spray of a fountain works just like raindrops suspended in the sky. Find the shadow of your head—that establishes the imaginary line. Then look 42 degrees away from that line. If there are enough raindrops in that direction, you’ll spy the red band of the rainbow and then the rest of the bow will come immediately into view. It’s rare that you see a full semicircular arc in a fountain—the only way you can see one is to be very close to the fountain—but the sight is so beautiful, it’s always worth trying.
一旦你找到了它，我得提醒你，你可能会忍不住想告诉其他行人。我经常指着这些喷泉彩虹给路人看，我敢肯定有些人觉得我很奇怪。但就我而言，为什么只有我才能欣赏到这隐藏的美景呢？奇观？我当然会带别人去看。如果你知道彩虹可能就在你眼前，为什么不去找找呢？为什么不让别人也看到呢？它们真的太美了。
Once you’ve found it, I warn you that you may just feel the urge to let your fellow pedestrians know it’s there. I often point these fountain rainbows out to passersby, and I’m sure some of them think I’m weird. But as far as I’m concerned, why should I be the only one to enjoy such hidden wonders? Of course I show them to people. If you know a rainbow could be right in front of you, why not look for it, and why not make sure others see it too? They are just so beautiful.
学生们经常问我，是否存在第三道弓。答案是既有又没有。正如你可能已经猜到的，第三道弓是由雨滴内部的三次反射形成的。这道弓的中心是太阳，与中心位于反日点的主弓一样，它的半径也约为42度，红色位于外侧。因此，你必须朝着太阳的方向看才能看到它，而且你和太阳之间必须有雨水。但即便如此，你几乎也看不到太阳。还有其他问题：大量的阳光会穿过雨滴而不发生任何反射，这会在太阳周围形成非常明亮且范围很广的光晕，使得第三道弓几乎无法被观测到。第三道弓比第二道弓还要暗淡。它也比主弓和第二道弓都要宽广得多；因此，原本就微弱的光线会更加分散在天空中，这使得观测它变得更加困难。据我所知，目前还没有关于三级弓的图片，我也不知道有谁见过三级弓。然而，确实有一些目击报告。
Students often ask me whether there is also a tertiary bow. The answer is yes and no. The tertiary bow results, as you might have guessed, from three reflections inside the raindrop. This bow is centered on the Sun and, like the primary bow, which is centered on the antisolar point, it also has a radius of about 42 degrees and red is on the outside. Thus you have to look toward the Sun to see it and it has to rain between you and the Sun. But when that is the case, you will almost never see the Sun. There are additional problems: a lot of sunlight will go through the raindrops without reflecting at all and that produces a very bright and very large glow around the Sun which makes it effectively impossible to see the tertiary bow. The tertiary bow is even fainter than the secondary. It is also much broader than the primary and the secondary bow; thus the already faint light of the bow is spread out even more over the sky and that makes it even more difficult to see it. As far as I know, no pictures of tertiary bows exist, and I do not know of anyone who has ever seen a tertiary bow. Yet there are some reports of sightings.
人们总是想知道彩虹是否真实存在。他们会想，也许彩虹只是海市蜃楼，随着我们靠近而不断远去。毕竟，为什么我们看不到彩虹的尽头呢？如果你也曾有过这样的疑问，那就放心吧。彩虹是真实存在的，它是阳光与雨滴相互作用，最终汇聚成你眼睛的产物。但由于彩虹的形成需要你的眼睛、太阳和雨滴的精确配合，所以你看到的彩虹和街对面的人看到的彩虹会有所不同。它们同样真实，只是形态不同。
Inevitably, people want to know if rainbows are real. Maybe they’re mirages, they wonder, receding endlessly as we approach them. After all, why can’t we see the end of the rainbow? If this thought has been at the back of your mind, breathe easy. Rainbows are real, the result of real sunlight interacting with real raindrops and your real eyes. But since they result from a precise collaboration between your eyes, the Sun, and the raindrops, you will see a different rainbow from the person across the street. Equally real, but different.
我们通常看不到彩虹的尽头，并非因为它不存在，而是因为它距离太远，或者被建筑物、树木或山脉遮挡，又或者那里的雨滴较少，彩虹太过微弱。但如果你能足够靠近彩虹，甚至可以触摸到它，就像你用花园水管制造的彩虹一样。
The reasons we usually cannot see the end of the rainbow touching the Earth are not because it doesn’t exist, but because it’s too far away, or hidden by buildings or trees or mountains, or because there are fewer raindrops in the air there and the bow is too faint. But if you can get close enough to a rainbow, you can even touch it, which you should be able to do with the rainbow you make with your garden hose.
我甚至在淋浴时会把彩虹捧在手里。这完全是偶然发现的。那天我迎着淋浴喷头，突然看到淋浴间里出现了两道（没错，是两道！）明亮的主彩虹，每道大约一英尺长，一英寸宽。这真是太令人兴奋、太美了，简直像做梦一样。我伸出手，把它们捧在了手里。那种感觉真是妙不可言！我讲授彩虹已经四十年了，却从未见过两道主彩虹如此近在咫尺。
I have even taken to holding rainbows in my hand while I shower. I accidentally discovered this one day. When I faced the shower spray, I suddenly saw two (yes two!) bright primary rainbows inside my shower, each one about a foot long and an inch wide. This was so exciting, so beautiful; it was like a dream. I reached out and held them in my hands. Such a feeling! I’d been lecturing on rainbows for forty years, and never before had I seen two primary rainbows within arm’s reach.
事情是这样的：一缕阳光透过浴室窗户照进我的淋浴间。某种程度上，我感觉自己不是站在喷泉前，而是站在喷泉里。由于水离我很近，而且我的双眼相距大约三英寸，所以每只眼睛都看到了各自独立的一条假想线。角度恰到好处，水量也恰到好处，我的每只眼睛都看到了各自的主彩虹。当我闭上一只眼睛时，其中一道彩虹就消失了；当我闭上另一只眼睛时，另一道彩虹也消失了。我很想拍下这令人惊叹的景象，但我做不到，因为我的相机只有一个“眼睛”。
Here’s what had happened. A sliver of sunlight had shone into my shower through the bathroom window. In a way, it was as though I was standing not in front of a fountain, but inside the fountain. Since the water was so close to me and since my eyes are about three inches apart, each eye had its own, distinct imaginary line. The angles were just right, the amount of water was just right, and each of my eyes saw its own primary rainbow. When I closed one eye, one of the rainbows would disappear; when I closed the other eye, the other bow vanished. I would have loved to photograph this astonishing sight, but I couldn’t because my camera has only one “eye.”
那天离彩虹那么近，让我对它们的真实性有了全新的认识。我转动头部，它们也随之转动；但只要我的头保持不动，它们也纹丝不动。
Being so close to those rainbows that day made me appreciate in a new way just how real they were. When I moved my head, they too moved, but as long as my head stayed where it was, so did they.
我偶尔会尽可能地选择早晨淋浴的时间，以便欣赏这些彩虹。太阳必须在天空中处于合适的位置，才能以合适的角度透过我家浴室的窗户照射进来，而这种情况只发生在五月中旬到七月中旬之间。你可能知道，在某些月份，太阳升起得更早，位置也更高；在北半球，冬季太阳升起的位置更偏南（东），夏季则更偏北（东）。
Occasionally I time my morning showers whenever possible to catch these rainbows. The Sun has to be at the right location in the sky to peek through my bathroom window at the right angle and this only happens between mid-May and mid-July. You probably know that the Sun rises earlier and goes higher in the sky in certain months, and that in the Northern Hemisphere it rises more to the south (of east) than in the winter months, and more to the north (of east) in summer.
我的浴室窗户朝南，南边有一栋楼，所以正南方向的光线根本照不进来。阳光只能大致从东南方向照射进来。我第一次看到淋浴彩虹是在很晚的时候，大概十点钟左右，当时我正在洗澡。想要在自己的淋浴间看到彩虹，你需要……浴室窗户必须能让阳光照射到喷头上。事实上，如果你从浴室窗户根本看不到太阳，那就没必要寻找淋浴喷头了——根本不可能。阳光必须能够真正照射到淋浴喷头上。即使阳光直射进来，也不能保证一定有效，因为很多水滴必须以与你想象中的直线成 42 度角的方向照射进来，而实际情况可能并非如此。
My bathroom window faces south, and there’s a building on the south side, making sure that light can never enter from due south. So sunlight only comes in roughly from the southeast. The time I first saw the shower bows was while I was taking a very late shower, around ten o’clock. In order to see rainbows in your own shower you will need a bathroom window through which sunlight can reach the spray. In fact, if you can never see the Sun by looking out your bathroom window, there’s no point in looking for shower bows—there just won’t be any. The sunlight must be able to actually reach your shower. And even if it does come directly in, that’s no guarantee, because many water drops have to be present at 42 degrees from your imaginary line, and that may not be the case.
这些条件或许很难满足，但为什么不试试呢？如果你发现傍晚时分阳光正好照进你的淋浴间，那么，你或许可以考虑调整一下淋浴时间。
These are probably difficult conditions to meet, but why not try? And if you discover that the Sun enters your shower just right late in the afternoon, well, then, you could always think about changing your shower schedule.
水手为什么戴太阳镜
Why Sailors Wear Sunglasses
当你决定去寻找彩虹时，如果你的太阳镜是偏光镜，一定要摘下来，否则你可能会错过这场美景。我曾经有过一次有趣的经历。正如我之前所说，我喜欢在普拉姆岛的海滩上散步。我也解释过如何在海浪的飞溅中看到小小的彩虹。几年前，我沿着海滩散步。阳光灿烂，微风拂面，海浪拍打着海岸，溅起很多水花——所以我经常看到一些小小的彩虹碎片，就像我在本章前面提到的那样。我开始指给我的朋友看，但他却说他看不到我在说什么。我们就这样来回说了不下六次。“那里有一个！”我有点恼火地喊道。“我什么也没看到！”他大声回应。但就在这时，我灵光一闪，让他摘下太阳镜，我看了看——果然，那是一副偏光太阳镜。他摘下墨镜后看到了蝴蝶结，甚至还指给我看！这到底是怎么回事？
Whenever you do decide to go rainbow hunting, be sure to take off your sunglasses if they are the kind we call polarized, or you might miss out on the show. I had a funny experience with this one day. As I said, I love to take walks along the beaches of Plum Island. And I’ve explained how you can see little bows in the spray of the waves. Years ago I was walking along the beach. The sun was bright and the wind was blowing, and when the waves rolled over as they got close to the beach, there was lots of spray—so I was frequently seeing small pieces of bows as I mentioned earlier in this chapter. I started pointing them out to my friend, who said he couldn’t see what I was talking about. We must have gone back and forth half a dozen times like this. “There’s one,” I would shout, somewhat annoyed. “I don’t see anything!” he would shout back. But then I had a bright moment and I asked him to take off his sunglasses, which I looked at—sure enough, they were polarized sunglasses. Without his sunglasses he did see the bows, and he even started to point them out to me! What was going on?
彩虹是自然界中一种奇特的现象，因为几乎所有的光线都是偏振光。你可能知道“偏振”这个词的含义。太阳镜的描述。这个术语在技术上并不完全准确，但让我先解释一下偏振光——之后我们再来谈谈太阳镜和彩虹。
Rainbows are something of an oddity in nature because almost all of their light is polarized. Now you probably know the term “polarized” as a description of sunglasses. The term is not quite technically correct, but let me explain about polarized light—then we’ll get to the sunglasses and rainbows.
波是由“某种东西”的振动产生的。振动的音叉或小提琴弦会产生声波，我将在下一章讨论声波。光波是由振动的电子产生的。当振动方向完全一致且垂直于波的传播方向时，我们称这种波为线偏振波。为了简便起见，下文将省略“线偏振”一词，因为本章仅讨论这种偏振光。
Waves are produced by vibrations of “something.” A vibrating tuning fork or violin string produces sound waves, which I talk about in the next chapter. Light waves are produced by vibrating electrons. Now, when the vibrations are all in one direction and are perpendicular to the direction of the wave’s propagation, we call the waves linearly polarized. For simplicity I will drop the term “linearly” in what follows as I am only talking in this chapter about this kind of polarized light.
声波永远不可能偏振，因为它们总是沿着压力波中振动的空气分子的方向传播；就像弹簧玩具产生的波一样。然而，光可以偏振。阳光或家里的灯泡发出的光都不是偏振光。但是，我们可以很容易地将非偏振光转换为偏振光。一种方法是购买所谓的偏光太阳镜。现在你知道为什么它们的名字不太准确了吧。它们实际上是偏光太阳镜。另一种方法是购买线性偏光片（由宝丽来公司创始人埃德温·兰德发明），然后透过它观察世界。兰德的偏光片通常厚1毫米，并且有各种尺寸。几乎所有穿过这种偏光片的光（包括偏光太阳镜发出的光）都会变成偏振光。
Sound waves can never be polarized, because they always propagate in the same direction as the oscillating air molecules in the pressure waves; like the waves you can generate in a Slinky. Light, however, can be polarized. Sunlight or light from lightbulbs in your home is not polarized. However, we can easily convert nonpolarized light into polarized light. One way is to buy what are known as polarized sunglasses. You now know why their name isn’t quite right. They are really polarizing sunglasses. Another is to buy a linear polarizer (invented by Edwin Land, founder of the Polaroid Corporation) and look at the world through it. Land’s polarizers are typically 1 millimeter thick and they come in all sizes. Almost all the light that passes through such a polarizer (including polarizing sunglasses) has become polarized.
如果你把两个矩形偏振片叠放在一起（我会给每个学生发两个，让他们回家做实验），然后把它们旋转90度，就不会有光线通过。
If you put two rectangular polarizers on top of each other (I hand out two of them to each of my students, so they can experiment with them at home) and you turn them 90 degrees to each other, no light will pass through.
自然界无需借助兰德的偏振器就能产生大量的偏振光。来自与太阳方向成90度角的蓝天的光线几乎完全偏振。我们如何判断呢？透过一块线性偏振片观察蓝天（任何与太阳方向成90度角的位置），并缓慢旋转偏振片。你会注意到天空的亮度会发生变化。当天空几乎完全变暗时，来自天空该部分的光线就会发生偏振。几乎完全偏振。因此，要识别偏振光，你只需要一个偏振器（但有两个偏振器会更有趣）。
Nature produces lots of polarized light without the help of one of Land’s polarizers. Light from the blue sky 90 degrees away from the direction of the Sun is nearly completely polarized. How can we tell? You look at the blue sky (anywhere at 90 degrees away from the Sun) through one linear polarizer and rotate it slowly while looking through it. You will notice that the brightness of the sky will change. When the sky becomes almost completely dark, the light from that part of the sky is nearly completely polarized. Thus, to recognize polarized light, all you need is one polarizer (but it’s much more fun to have two).
在第一章中，我描述了如何在课堂上通过香烟烟雾散射白光来“制造”蓝光。我特意布置了装置，使散射到教室里的蓝光以大约90度的角度散射；它也几乎完全偏振。学生们可以用他们自己带去上课的偏振器来观察这一点。
In the first chapter I described how in class I “create” blue light by scattering white light off cigarette smoke. I arrange this in such a way that the blue light that scatters into the lecture hall has scattered over an angle of about 90 degrees; it too is nearly completely polarized. The students can see this with their own polarizers, which they always bring with them to lectures.
当阳光（或灯泡发出的光线）以特定角度（我们称之为布儒斯特角）照射到水面或玻璃表面时，反射的阳光几乎会完全偏振。这就是为什么船员和水手要佩戴偏光太阳镜的原因——它们可以阻挡大部分从水面反射的光线。（大卫·布儒斯特是19世纪苏格兰物理学家，他在光学领域进行了大量研究。）
Sunlight that has been reflected off water or glass can also become nearly completely polarized if the sunlight (or light from a lightbulb) strikes the water or glass surface at just the right angle, which we call the Brewster angle. That’s why boaters and sailors wear polarizing sunglasses—they block much of the light reflecting off the water’s surface. (David Brewster was a nineteenth-century Scottish physicist who did a lot of research in optics.)
我的钱包里总是至少放着一个偏光镜——是的，总是——我也敦促我的学生们这样做。
I always carry at least one polarizer with me in my wallet—yes, always—and I urge my students to do the same.
我为什么要跟你们讲这么多关于偏振光的知识呢？因为彩虹中的光几乎完全是偏振光。偏振现象发生在阳光被水滴反射的时候，而你们现在也知道，这是彩虹形成的必要条件。
Why am I telling you all this about polarized light? Because the light from rainbows is nearly completely polarized. The polarization occurs as the sunlight inside the water drops reflects, which, as you now know, is a necessary condition for rainbows to be formed.
我在课堂上会用一滴很大的水滴制作一种特殊的彩虹，并能演示以下现象：（1）彩虹外侧是红色，（2）内侧是蓝色，（3）彩虹内侧的光明亮而呈白色，而外侧则不是，（4）彩虹发出的光是偏振光。彩虹的偏振特性令我着迷（这也是我总是随身携带偏振器的原因之一）。您可以在我的讲座视频中看到这个精彩的演示：http: //ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-22/。
I make a special kind of rainbow in my classes (using a single, though very large, water drop) and I am able to demonstrate that (1) red is on the outside of the bow, (2) blue is on the inside, (3) inside the bow the light is bright and white, which is not the case outside the bow, and (4) the light from the bow is polarized. The polarization of the bows for me is very fascinating (one reason why I always carry polarizers on me). You can see this wonderful demonstration in my lecture at http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-22/.
彩虹之外
Beyond the Rainbow
彩虹是最广为人知、色彩最绚丽的大气奇观，但它们绝非孤例。大气现象种类繁多，有些奇特而引人注目，有些则神秘莫测。不过，我们还是先来看看彩虹，看看它们会带我们去哪里吧。
Rainbows are the best known and most colorful atmospheric creations, but they are far from alone. There is an entire host of atmospheric phenomena, some of them really quite strange and striking, others deeply mysterious. But let’s stay with rainbows for a bit and see where they take us.
当你仔细观察一道非常明亮的彩虹时，有时会在其内缘看到一系列明暗相间的条纹——这些条纹被称为副虹。你可以在插图中看到一个。要解释副虹，我们必须放弃牛顿对光线的解释。他认为光是由粒子组成的，因此当他想象光线进入雨滴、在雨滴中反射并最终离开时，他假设这些光线就像微小的粒子一样。但为了解释副虹，我们需要将光视为波。而要形成副虹，光波必须穿过非常小的雨滴，其直径小于一毫米。
When you look carefully at a very bright rainbow, on its inner edge you may sometimes see a series of alternating bright-colored and dark bands—which are called supernumerary bows. You can see one in the insert. To explain these we must abandon Newton’s explanation of light rays. He thought that light was composed of particles, so when he imagined individual rays of light entering, bouncing around in, and exiting raindrops, he assumed that these rays acted as though they were little particles. But in order to explain supernumerary bows we need to think of light as consisting of waves. And in order to make a supernumerary bow, light waves must go through raindrops that are really small, smaller than a millimeter across.
物理学中最重要的实验之一（通常被称为双缝实验）证明了光是由波组成的。在这个著名的实验中（大约在1801-1803年间），英国科学家托马斯·杨将一束窄光束分成两束，并在屏幕上观察到一个图案（两束光的叠加），这个图案只有用光是由波组成的才能解释。后来，人们用两个狭缝（或两个针孔）以不同的方式进行了这个实验。在这里，我假设一束窄光束照射到一张薄纸板上两个非常小的（彼此靠近的）针孔上。光线穿过针孔，然后照射到屏幕上。如果光是由粒子组成的，那么一个给定的粒子要么穿过一个针孔，要么穿过另一个针孔（它不可能同时穿过两个针孔），因此你会在屏幕上看到两个亮点。然而，观察到的图案却截然不同。它与你的预期完全吻合。如果两束光波同时照射到屏幕上——一束光波来自一个针孔，另一束完全相同的光波同时来自另一个针孔。两束光波叠加会发生干涉现象。当一个针孔发出的光波的波峰与另一个针孔发出的光波的波谷重合时，两束光波会相互抵消，这称为相消干涉，屏幕上发生相消干涉的区域（有好几个）会保持黑暗。是不是很神奇——光加光竟然变成了黑暗！另一方面，在屏幕上其他两束光波同步的位置，波峰和波谷同时出现，就会发生相长干涉，屏幕上会出现亮斑（也有好几个）。因此，屏幕上会出现明暗交替的图案，这正是杨氏分束实验所观察到的现象。
One of the most important experiments in all of physics (generally referred to as the double-slit experiment) demonstrated that light is made of waves. In this famous experiment performed around 1801–03, the English scientist Thomas Young split a narrow beam of sunlight into two beams and observed on a screen a pattern (the sum of the two beams) that could only be explained if light consists of waves. Later in time this experiment was done differently actually using two slits (or two pinholes). I will proceed here assuming that a narrow beam of light strikes two very small pinholes (close together) made in a thin piece of cardboard. The light passes through the pinholes and then strikes a screen. If light was made of particles, a given particle would either go through one pinhole or through the other (it cannot go through both) and thus you would see two bright spots on the screen. However, the pattern observed is very different. It precisely mimics what you’d expect if two waves had hit the screen—one wave coming from one pinhole and simultaneously one identical wave coming from the other. Adding two waves is subject to what we call interference. When the crests of the waves from one pinhole line up with the valleys of waves from the other, the waves cancel each other, which is called destructive interference, and the locations on the screen where that happens (and there are several) remain dark. Isn’t that amazing—light plus light turns into darkness! On the other hand, at other locations on the screen where the two waves are in sync with one another, cresting and falling with one another, we have constructive interference and we end up with bright spots (and there will be several). Thus we will see a spread out pattern on the screen consisting of alternating dark and bright spots, and that is precisely what Young observed with his split-beam experiment.
我在课堂上用红色激光和绿色激光演示过这个现象，效果非常壮观。学生们注意到，绿光的图案与红光非常相似，只是绿光中明暗斑点之间的距离略小一些。这种距离取决于光的颜色（也就是波长）（下一章会详细介绍波长）。
I demonstrate this in my classes using red laser light and also with green laser light. It’s truly spectacular. Students notice that the pattern of the green light is very similar to that of the red light except that the separation between the dark and the bright spots is somewhat smaller for the green light. This separation depends on the color (thus wavelength) of light (more about wavelength in the next chapter).
几个世纪以来，科学家们一直在争论光是由粒子还是波构成的，而这项实验带来了惊人的发现。无可辩驳的结论是，光是一种波。我们现在知道，光既可以表现为粒子，也可以表现为波，但这个惊人的结论还要再等一个世纪，直到量子力学的发展才得以实现。目前我们无需对此进行更深入的探讨。
Scientists had been battling for centuries over whether light consisted of particles or waves, and this experiment led to the stunning and indisputable conclusion that light is a wave. We now know that light can act both as a particle and as a wave, but that astounding conclusion had to wait another century, for the development of quantum mechanics. We don’t need to go further into that at the moment.
回到副虹现象，光波的干涉是形成明暗条纹的原因。当液滴直径接近0.5毫米时，这种现象非常明显。您可以在www.atoptics.co.uk/rainbows/supdrsz.htm上看到一些副虹现象的图片。
Going back to supernumerary bows, interference of light waves is what creates the dark and bright bands. This phenomenon is very pronounced when the diameter of the drops is near 0.5 millimeters. You can see some images of supernumerary bows at www.atoptics.co.uk/rainbows/supdrsz.htm.
当液滴直径小于约40微米（0.04毫米，或1/635英寸）时，干涉效应（通常称为衍射）会变得更加显著。此时，不同颜色的光波会扩散得非常厉害，以至于它们完全重叠；颜色混合在一起，彩虹就变成了白色。白色彩虹通常会带有一两条暗带（副虹）。它们非常罕见，我从未亲眼见过。我的学生卡尔·威尔士在20世纪70年代中期给我寄来了几张美丽的白色彩虹的照片。这些照片是他夏天凌晨两点（没错，就是凌晨两点）在弗莱彻冰岛拍摄的，弗莱彻冰岛是一座巨大的漂浮冰山（大约3×7英里）。当时，它距离北极点大约300英里。您可以在插图中看到一张漂亮的白色彩虹照片。
The effects of interference (often called diffraction) become even more dramatic when the diameters of the droplets are smaller than about 40 microns (0.04 millimeters, or 1/635 of an inch). When that happens, the colors spread out so much that the waves of different colors completely overlap; the colors mix and the rainbow becomes white. White rainbows often show one or two dark bands (supernumerary bows). They are very rare and I have never seen one. A student of mine, Carl Wales, sent me pictures in the mid-1970s of several beautiful white rainbows. He had taken the pictures in the summer at two a.m. (yes, two a.m.) from Fletcher Ice Island, which is a large drifting iceberg (about 3 × 7 miles). At the time, it was about 300 miles from the North Pole. You can see a nice picture of a white rainbow in the insert.
这些白色的雾虹也出现在雾中，雾是由极其细小的水滴组成的。雾虹很难被发现；你可能已经见过很多次却没注意到。当雾足够稀薄，阳光可以穿透时，它们就容易出现。清晨，当太阳低垂，雾气弥漫时，我常常在河岸边或港口寻找雾虹，也因此见过不少。
These white bows can also be seen in fog, which consists of exceptionally tiny water droplets. White fogbows can be hard to spot; you may have seen them many times without realizing it. They are likely to appear whenever fog is thin enough for sunlight to shine through it. When I’m on a riverbank or in a harbor in the early morning, when the Sun is low in the sky, and where fog is common, I hunt for them and I have seen many.
有时候，你甚至可以用车灯投射出雾虹。如果你正在开车，夜雾弥漫，看看能不能找到安全的地方停车。或者，如果你在家，雾气袭来，就把车头朝向雾气，打开车灯。然后离开车辆，观察车灯照射到的雾气。如果你运气好的话，你或许能看到雾虹。它们让雾夜的阴沉更添几分诡异。你可以访问www.extremeinstability.com/08-9-9.htm ，看看一位朋友用汽车前灯偶然发现的雾虹。你注意到白色彩虹上的暗色条纹了吗？
Sometimes you can even create a fogbow with your car headlights. If you’re driving and the night fog rolls in around you, see if you can find a safe place to park. Or, if you’re at home and the fog comes, face your car toward the fog and turn on your headlights. Then walk away from your car and look at the fog where your headlight beams are. If you’re lucky, you might be able to see a fogbow. They make the gloom of a foggy night even spookier. You can see the results of a fellow stumbling across fogbows that he made with his car headlights at www.extremeinstability.com/08-9-9.htm. Did you notice the dark bands in the white bows?
水滴的大小和光的波动性也解释了天空中另一种最美丽的现象：云辉。飞越云层时是观赏云辉的最佳时机。相信我，绝对值得一试。当然，要做到这一点，你必须坐在靠窗的座位上——而不是机翼上方，因为机翼会遮挡你的视线。你需要确保太阳位于飞机与你座位相对的一侧，所以你必须注意飞行时间和飞行方向。如果你能透过窗户看到太阳，实验就结束了。（我必须请你相信我；要给出令人信服的解释需要非常复杂的数学。）如果满足了这些条件，那么试着找出反日点的位置，并向下观察它。如果你运气好，可能会在云层中看到彩色光环；如果你的飞机飞得离云层不太远，甚至可能看到光环围绕着飞机的影子旋转——光环的直径从几度到大约20度不等。水滴越小，光环就越大。
The size of water droplets and the wave nature of light also explain another of the most beautiful phenomena that grace the skies: glories. They can best be seen when flying over clouds. Trust me, it’s worth trying to find them. In order to do so, you must, of course, be in a window seat—and not over the wings, which block your view down. You want to make certain that the Sun is on the side of the plane opposite your seat, so you’ll have to pay attention to the time of day and the direction of the flight. If you can see the Sun out your window, the experiment is over. (I have to ask you to trust me here; a convincing explanation requires a lot of very complicated math.) If these conditions are met, then try to figure out where the antisolar point is and look down at it. If you’ve hit the jackpot you may see colorful rings in the clouds and if your plane is flying not too far above the clouds, you may even see the glory circling the shadow of the plane—glories have diameters that can vary from a few degrees to about 20 degrees. The smaller the drops, the larger the glories.
我拍了很多日冕洞的照片，其中一些照片里我的飞机影子清晰可见。更有趣的是，我的座位正好位于日冕洞的中心，也就是反日点。其中一张照片就放在插图里。
I have taken many pictures of glories, including some where the shadow of my plane was clearly visible and the really fun part is that the position of my seat is at the center of the glory, which is the antisolar point. One of these pictures is in the insert.
你不仅能在飞机上看到光环，在各种地方都能看到它们。徒步旅行者背对太阳，俯瞰雾气弥漫的山谷时，也常常能看到它们。在这种情况下，会出现一种颇为诡异的景象：他们看到自己的影子投射在雾气中，周围环绕着光环，有时甚至会出现几圈色彩斑斓的光环，看起来宛如幽灵一般。这种现象也被称为布罗肯幽灵（或布罗肯弓），得名于德国一座经常出现光环的高峰。事实上，人们影子周围的光环看起来非常像圣洁的光环，而这些光环本身又显得如此超凡脱俗，因此，你或许不会惊讶地发现，“glory” （光环）实际上是一个古老的词汇。指的是环绕在各圣人头顶的光环。在中国，这种光环被称为佛光。
You can find glories in all kinds of places, not just from airplanes. Hikers often see them when they have the Sun to their backs and look down into misty valleys. In these cases, a quite spooky effect happens. They see their own shadow projected onto the mist, surrounded by the glory, sometimes several colorful rings of it, and it looks positively ghostly. This phenomenon is also known as the Brocken spectre (also called Brocken bow), named for a high peak in Germany where sightings of glories are common. In fact, glories around people’s shadows look so much like saintly halos, and the figures themselves look so otherworldly, that you will not be surprised to learn that glory is actually an old word for the circle of light around the heads of various saints. In China, glories are known as Buddha’s light.
我曾拍过一张绝妙的照片，照片里我的影子被一片光辉环绕，我称之为圣瓦尔特的影像。很多年前，我受邀去参观几位俄罗斯天文学家朋友位于高加索山脉的6米望远镜。这在当时是世界上最大的望远镜。那里的天气实在太糟糕了，根本不适合观测。我每天下午五点半左右，都会有一堵浓雾从山谷里滚滚而来，彻底遮蔽了望远镜。我是说真的，完全被雾气笼罩了；在我参观期间，我们根本无法进行任何观测。插图里有一张雾气升腾的照片。和天文学家们交谈后，我得知这种雾气很常见。于是我问：“那为什么还要把望远镜建在这里呢？”他们告诉我，望远镜之所以建在这里，是因为一位党政官员的妻子想要把它建在这里，事情就是这样。我当时差点从椅子上摔下来。
I once took a marvelous photo of my own shadow surrounded by a glory that I refer to as the image of Saint Walter. A good many years ago I was invited by some of my Russian astronomer friends to their 6-meter telescope in the Caucasus Mountains. This was the world’s largest telescope at the time. The weather was just awful for observing. Every day I was there, at about five thirty in the afternoon a wall of fog would come rolling up out of the valley below and completely engulf the telescope. I mean totally; we couldn’t make any observations at all during my visit. A picture of the fog ascending is shown in the insert. In talking to the astronomers, I learned that the fog was very common. So I asked, “Why then was this telescope built here?” They told me that the telescope was built on that site because the wife of a Party official wanted it right there, and that was that. I almost fell off my chair.
总之，几天后，我突然想到或许能拍到一张绝妙的照片。每天，当雾气从东边的山谷升起时，太阳依然在西边高悬，这正是拍摄日冕洞的完美时机。于是第二天，我带着相机来到天文台，心里忐忑不安，担心雾气会不配合。但果不其然，雾墙渐渐浓厚起来，太阳依旧高照，而我背对着它。我耐心地等待着，突然，日冕洞出现在我的影子周围，我立刻按下快门。我迫不及待地冲洗胶卷——那时还是数码时代之前——照片就在那里！我的影子又长又飘渺，而相机的影子则恰好位于绚丽日冕洞光环的中心。你可以在插图中看到这张照片。
Anyway, after a few days, I got the idea that I might be able to take a fantastic photo. The Sun was still strong in the west every day when the fog came up from the valley, which was to the east, the perfect setup for glories. So the next day I brought my camera to the observatory, and I was getting nervous that the fog might not cooperate. But sure enough, the wall of fog swelled up, and the Sun was still shining, and my back was to it. I waited and waited and then, boom, there was the glory around my shadow and I snapped. I couldn’t wait to develop the film—this was in the pre-digital age—and there it was! My shadow is long and ghostly, and the shadow of my camera is at the center of the rings of a gorgeous glory. You can see the picture in the insert.
你无需身处异域风情之地才能看到头顶的光环。在阳光明媚的清晨，如果你仰望一片沾满露水的草地，观察自己投射在草地上的影子（当然，太阳要在你身后），你通常可以看到德语中被称为“ Heiligenschein ”（圣光）的现象：头顶影子周围环绕着一圈光晕。（它并非五彩斑斓，也不是圣光。）草地上的露珠反射阳光，从而产生了这种效果。如果你尝试一下——我希望你能试试——你会发现它们比圣光更容易找到。你会发现，由于现在是清晨，太阳位置较低，你的影子会很长，看起来很像中世纪艺术中那些身形修长、头顶光环的圣徒。
You don’t need to be in such an exotic location to see a halo around your head. On a sunlit early morning if you look at your shadow on a patch of dewy grass (of course with the Sun right behind you), you can often see what in German is called Heiligenschein, or “holy light”: a glow around the shadow of your head. (It’s not multicolored; it’s not a glory.) Dewdrops on the grass reflect the sunlight and create this effect. If you try this—and I hope you will—they’re easier to find than glories. You will see that since it’s early morning and the Sun is low, your shadow will be quite long, and you appear much like the elongated and haloed saints of medieval art.
各种各样的弓形光晕和光环常常在最意想不到的地方出现，给你带来惊喜。我最喜欢的一次目击发生在2004年6月一个阳光明媚的日子——我记得那天是夏至，6月21日——当时我和苏珊（那时她还不是我的妻子）、我的儿子以及他的女朋友一起参观位于马萨诸塞州林肯市的德科多瓦博物馆。我们正穿过博物馆的庭院走向入口，儿子突然叫住了我。只见在我们面前的地面上，出现了一个令人惊艳的、色彩斑斓的、近乎圆形的弓形光晕。（因为是夏至，太阳在波士顿的位置达到了一年中最高的高度，大约在地平线以上70度。）真是美得令人窒息！
The many different types of bows and halos can surprise you in the most unexpected places. My favorite sighting happened one sunny day in June 2004—I remember it was the summer solstice, June 21—when I was visiting the deCordova Museum in Lincoln, Massachusetts, with Susan (who was not yet my wife at the time), my son, and his girlfriend. We were walking across the grounds toward the entrance when my son called out to me. There in front of us, on the ground, was a stunning, colorful, nearly circular bow. (Because it was the solstice, the Sun was as high as it ever gets in Boston, about 70 degrees above the horizon.) It was breathtaking!
我赶紧拿出相机，以最快的速度拍了一堆照片。真是出乎意料。地上没有水滴，而且我很快意识到，无论如何，这道弧线都不可能是水滴形成的，因为它的半径远小于42度。然而，它看起来却像一道彩虹：红色在外，蓝色在内，而且弧线内部还有明亮的白光。这究竟是什么造成的呢？我意识到它一定是某种透明的球形颗粒构成的，但这些颗粒究竟是什么呢？
I pulled out my camera and snapped a bunch of photos as quickly as I could. How unexpected. There were no water droplets on the ground, and I quickly realized the bow could not have been made from water drops in any event because the radius of the bow was much smaller than 42 degrees. And yet it looked just like a rainbow: the red was on the outside, the blue was on the inside, and there was bright white light inside the bow. What could have caused it? I realized that it must have been made by transparent, spherical particles of something, but what could they be?
我在插图中拍摄的弓的照片之一效果非常好，以至于它成为了美国宇航局 (NASA) 2004 年 9 月 13 日在网上发布的每日天文神秘照片。（顺便说一句，这是一个很棒的网站，你应该每天都看看：http: //apod.nasa.gov/apod/astropix.html。）我收到了大约三千条关于这张照片是什么的猜测。我最喜欢的回复是四岁的本杰明·盖斯勒（Benjamin Geisler）手写的一张纸条，上面写着：“我认为你的神秘照片是用光、蜡笔、马克笔和彩色铅笔创作的。” 这张纸条已发布在……我在麻省理工学院办公室外面的公告栏上贴着答案。所有答案中，大约有三十个方向正确，但只有五个完全正确。
One of my photographs of the bow, which you can see in the insert, turned out so well that it became NASA’s astronomical mystery picture of the day, posted on the web on September 13, 2004.* (This, by the way, is a terrific website, and you should look at it every day at http://apod.nasa.gov/apod/astropix.html.) I received about three thousand guesses as to what it was. My favorite response was a handwritten note from Benjamin Geisler, age four, who wrote, “I think your mystery photo is made by light, crayons, markers and colored pencils.” It’s posted on the bulletin board outside my office at MIT. Of all the answers, about thirty were on the right track, but only five were dead on.
解开这个谜题的最佳线索是，我们参观博物馆时，那里正在进行大量的施工。特别是，博物馆的墙壁正在进行大量的喷砂处理。我曾与马科斯·汉金（Markos Hankin）共事多年，他当时负责麻省理工学院的物理演示工作。他告诉我——我当时并不知道——有些喷砂工艺会用到玻璃珠。地上散落着许多细小的玻璃珠。我带了几勺回家。我们看到的其实是一个玻璃弓，现在它已经成为弓的一个正式类别，指的是由玻璃珠形成的弓；它的半径约为28度，但具体数值取决于玻璃的种类。
The best clue to this puzzle is that there was a good bit of construction going on at the museum when we visited. In particular, there had been a lot of sandblasting of the museum’s walls. Markos Hankin, who was in charge of the physics demonstrations at MIT and with whom I have worked for many years, told me—I didn’t know this at the time—that some kinds of sandblasting use glass beads. And there were lots of tiny glass beads lying on the ground. I had taken a few spoonfuls of the beads home. What we had seen was a glassbow, which has now become an official category of bow, a bow formed by glass beads; it has a radius of about 28 degrees, but the exact value depends on the kind of glass.
我和马科斯迫不及待地想看看能不能自己做一个，用在我的讲座上。我们买了好多磅玻璃珠，把它们粘在几张大黑纸上，然后把纸贴到阶梯教室的黑板上。接着，在我讲完彩虹之后，我们从教室后方用聚光灯照着那张纸。成功了！我邀请学生们一个接一个地走到教室前面，站在黑板前，让他们的影子正好落在自己专属的“玻璃彩虹”中央。
Markos and I couldn’t wait to see if we could make one of our own for my lectures. We bought several pounds of glass beads, glued them on big sheets of black paper, and attached the paper to a blackboard in the lecture hall. Then, at the end of my lecture on rainbows, we aimed a spotlight on the paper from the back of the lecture hall. It worked! I invited the students to come, one by one, to the front of the class, where they stood before the blackboard and cast their shadow smack in the middle of their own private glassbow.
这次体验对学生们来说真是太刺激了，你也想在家试试；制作玻璃弓其实并不难。当然，这取决于你的目标。如果你只是想看看弓的颜色，那就很简单。如果你想让整个弓环绕你的头部，那就需要花更多功夫了。
This was such a thrilling experience for the students that you might want to try it at home; making a glassbow is not too difficult. It does depend on what your objectives are. If you just want to see the colors of the bow, it’s quite easy. If you want to see the entire bow encircling your head it’s more work.
要制作一小块弓形图案，你只需要一块大约一平方英尺的黑色硬纸板、一些透明喷胶（我们用的是3M的Spray Mount Artist's Adhesive，但任何透明喷胶都可以）和一些透明的球形玻璃珠。玻璃珠必须是透明的球形。我们使用的是“粗玻璃珠喷砂介质”，直径在150到250微米之间，你可以在这里找到： http: //tinyurl.com/glassbeads4rainbow。
To see a small piece of the bow, all you need is a piece of black cardboard about one foot square, some clear spray adhesive (we used 3M’s Spray Mount Artist’s Adhesive, but any clear spray glue will do), and transparent spherical glass beads. They must be transparent and spherical. We used “coarse glass bead blast media,” with diameters ranging from 150 to 250 microns, which you can find here: http://tinyurl.com/glassbeads4rainbow.
在纸板上喷上胶水，然后撒上珠子。珠子之间的平均距离并不关键，但珠子越密集越好。小心这些珠子——最好在室外操作，以免珠子洒得满地都是。让胶水晾干，如果天气晴朗，就到室外进行操作。
Spray glue on your cardboard, and then sprinkle the beads on it. The average distance between the beads isn’t critical, but the closer the beads are, the better. Be careful with these beads—you probably want to do this outside so you don’t spill beads all over your floor. Let the glue dry, and if you have a sunny day, go outside.
确定一条假想线（从你的头顶到头顶阴影处）。将纸板放在这条线上的某个位置；这样你就能在纸板上看到你头部的影子（如果太阳低垂，你可以把纸板放在椅子上；如果太阳高悬，你可以把它放在地上——想想德科多瓦博物馆里的玻璃珠也是放在地上的）。你可以选择纸板离你头部的距离。假设你把它放在离头部1.2米（约4英尺）的地方。然后，将纸板沿垂直于假想线的方向移动约0.6米（2英尺）。你可以朝任何方向（左、右、上、下）移动！这样你就能看到玻璃弓的颜色。如果你想把纸板放得更远一些，比如1.5米（5英尺），那么你需要移动纸板约0.75米（2.5英尺）才能看到弓的颜色。你可能想知道我是怎么得出这些数字的。原因很简单，玻璃弓的半径大约是28度。
Establish the imaginary line (from your head to the shadow of your head). Place the cardboard somewhere on that line; thus you will see the shadow of your head on the cardboard (if the Sun is low in the sky, you could put the cardboard on a chair; if the Sun is high in the sky you could put it on the ground—remember the glass beads at the deCordova museum were also on the ground. You may select how far away from your head you place the cardboard. Let’s assume that you place it 1.2 meters (about 4 feet) away. Then move the cardboard about 0.6 meters (2 feet) away from the imaginary line in a direction perpendicular to the line. You may do that in any direction (left, right, up, down)! You will then see the colors of the glassbow. If you prefer to place the cardboard farther away, say 1.5 meters (5 feet), then you have to move the cardboard about 0.75 meters (2.5 feet) to see the colors of the bow. You may wonder how I arrived at these numbers. The reason is simple, the radius of a glassbow is about 28 degrees.
一旦你看到颜色，就可以沿着假想的线移动纸板，寻找弓的其他部分。这样，你就能像用花园水管一样，将整个圆形弓的各个部分一一描绘出来。
Once you see the colors, you can move the cardboard in a circle around the imaginary line to search for other parts of the bow. By so doing, you are mapping out the entire circular bow in portions, just as you did with the garden hose.
如果你想一次性看到环绕在你影子周围的整个弓形图案，你需要一块更大的黑色硬纸板——一平方米就足够了——并且在上面粘上更多的玻璃珠。将你的头部影子放在硬纸板的中心附近。如果硬纸板到你头部的距离约为80厘米（约2.5英尺），你就能立即看到整个玻璃弓形图案。如果你把硬纸板放得太远，例如1.2米（4英尺），你就看不到整个弓形图案了。选择权在你；祝你玩得开心！
If you want to see the entire bow around your shadow all at once, you’ll need a bigger piece of black cardboard—one full square meter will do—and with a lot more glass beads glued to it. Place the shadow of your head near the center of the cardboard. If the distance from the cardboard to your head is about 80 centimeters (about 2.5 feet), you will immediately see the entire glass bow. If you bring the cardboard too far out, e.g., 1.2 meters (4.0 feet), you will not be able to see the entire bow. The choice is yours; have fun!
如果不是晴天，你可以像我在课堂上那样，在室内进行这个实验：用一束强光——比如聚光灯——照射墙壁。把纸板用胶带粘好或挂起来。调整好位置，让光线在你身后，你的头部阴影位于一平方米纸板的中心。如果你站在距离纸板80厘米的地方，你应该能看到整个弓围绕着你的影子旋转。欢迎来到玻璃弓的世界！
If it’s not a sunny day, you can try the experiment indoors, as I did in lectures, by aiming a very strong light—like a spotlight—at a wall, on which you’ve taped or hung the cardboard. Position yourself so the light is behind you, and the shadow of your head is in the center of the one square meter cardboard. If you stand 80 centimeters away from the board, you should be able to see the entire bow circling your shadow. Welcome to the glass bow!
当然，我们无需了解彩虹、雾虹或玻璃虹的形成原理就能欣赏它们的美丽，但了解彩虹的物理原理确实能让我们拥有全新的视角（我称之为知识之美）。我们会更加敏锐地捕捉到那些细微的奇迹，比如在雾蒙蒙的清晨、淋浴时、漫步喷泉旁，或者当大家都在看电影时，透过飞机舷窗向外望去。我希望下次当你感觉彩虹即将出现时，你能背对太阳，将视线转向与太阳轴线相距约42度的方向，然后就能看到天空中那道绚丽彩虹的红色上缘。
We don’t need to understand why a rainbow or fogbow or glassbow is formed in order to appreciate its beauty, of course, but understanding the physics of rainbows does give us a new set of eyes (I call this the beauty of knowledge). We become more alert to the little wonders we might just be able to spot on a foggy morning, or in the shower, or when walking by a fountain, or peeking out of an airplane window when everyone else is watching movies. I hope you will find yourself turning your back to the Sun the next time you feel a rainbow coming on, looking about 42 degrees away from the imaginary line and spotting the red upper rim of a glorious rainbow across the sky.
我的预言是这样的：下次你看到彩虹时，你会仔细检查红色是否在外，蓝色是否在内；你会尝试寻找副虹，并确认颜色正好相反；你会发现主虹内部天空明亮，而外部则暗得多；如果你随身携带线性偏振镜（你应该一直带着），你还会发现两道彩虹都具有很强的偏振特性。你将无法抗拒这种诱惑。这就像一种会伴随你一生的“疾病”。这是我的错，但我无力治愈你，对此我一点也不后悔，真的！
Here’s my prediction. The next time you see a rainbow, you’ll check to make sure that red is on the outside, blue is on the inside; you’ll try to find the secondary bow and will confirm that the colors are reversed; you’ll see that the sky is bright inside the primary bow and much darker outside of it; and if you carry a linear polarizer on you (as you always should), you will confirm that both bows are strongly polarized. You won’t be able to resist it. It’s a disease that will haunt you for the rest of your life. It’s my fault, but I will not be able to cure you, and I’m not even sorry for that, not at all!
第六章
CHAPTER 6
弦乐与管乐的和谐
The Harmonies of Strings and Winds
我十岁的时候学过小提琴，但拉得一塌糊涂，一年后就放弃了。二十多岁的时候我又学了钢琴，结果还是一塌糊涂。我至今仍然无法理解人们是如何用十根手指在不同的手上识谱并演奏出音乐的。不过，我确实非常欣赏音乐，除了与音乐建立情感联系之外，我还通过物理学的角度理解了它。事实上，我热爱音乐的物理学，而这当然要从声音的物理学入手。
I took violin lessons as a ten-year-old, but I was a disaster and stopped after a year. Then in my twenties I took piano lessons, and I was a disaster again. I still cannot understand how people can read notes and convert them into music using ten fingers on different hands. I do appreciate music a lot, however, and in addition to having an emotional connection with it, I have come to understand it through physics. In fact, I love the physics of music, which starts, of course, with the physics of sound.
你可能知道，声音源于物体的一次或多次快速振动，例如鼓面、音叉或琴弦。这些振动显而易见，对吧？然而，当这些物体振动时，实际发生的情况却不那么明显，因为它通常是不可见的。
You probably know that sound begins with one or more very rapid vibrations of an object, like a drum surface or a tuning fork or a violin string. These vibrations are pretty obvious, right? What is actually happening when these things vibrate, however, is not so obvious, because it is usually invisible.
音叉的往复运动首先压缩其周围的空气。然后，当它反向运动时，则会使附近的空气减压。这种交替的推拉作用会在空气中产生波，即压力波，我们称之为声波。这种波以我们称之为声速的速度（约340米/秒）非常迅速地到达我们的耳朵。每秒（大约五秒一英里，或三秒一公里）。这是室温下空气中的声速。声速会因传播介质的不同而有很大差异。声速在水中比在空气中快四倍，在铁中比在空气中快十五倍。
The back and forth motion of a tuning fork first compresses the air that is closest to it. Then, when it moves the other way, it decompresses the nearby air. This alternate pushing and pulling creates a wave in the air, a pressure wave, which we call a sound wave. This wave reaches our ears very quickly, at what we call the speed of sound: about 340 meters per second (about a mile in five seconds, or a kilometer in three). This is the speed of sound in air at room temperature. It can differ a great deal, depending on the medium it’s traveling through. The speed of sound is four times faster in water and fifteen times faster in iron than in air.
光在真空中的速度（以及所有电磁辐射的速度）是一个著名的常数，称为c，约为每秒 300,000 公里（你可能学过它是每秒 186,000 英里），但可见光在水中的速度要慢大约三分之一。
The speed of light (and all electromagnetic radiation) in vacuum is a famous constant, known as c, about 300,000 kilometers per second (you may have learned it as 186,000 miles per second), but the speed of visible light is about a third slower in water.
现在让我们回到音叉。当它产生的波冲击我们的耳朵时，会以与音叉振动空气时完全相同的频率，推动我们的耳膜向内和向外振动。然后，经过一个近乎荒谬的复杂过程，耳膜振动带动中耳的听小骨（即锤骨、砧骨和镫骨）振动，这些听小骨又会在内耳的液体中产生波。这些波随后被转化为电神经冲动，传递到大脑，而大脑则将这些信号解读为声音。真是个相当复杂的过程。
Now to get back to the tuning fork. When the wave it produces hits our ears, it pushes our eardrums in and out at exactly the same rate of oscillations as the tuning fork presses on the air. Then, through an almost absurdly complicated process, the eardrum vibrates the bones of the middle ear, known wonderfully as the hammer, anvil, and stirrup, and they in turn produce waves in the fluid in the inner ear. These waves are then converted into electric nerve impulses sent to the brain, and your brain interprets these signals as sound. Quite a process.
声波——实际上所有波——都具有三个基本特征：频率、波长和振幅。频率是指单位时间内通过某一点的波的数量。如果你在船上或游轮上观察海浪，你可能会注意到，比如说，一分钟内有十个波浪经过，所以我们可能会说它们的频率是每分钟十个。但实际上，我们通常用每秒振荡次数来测量频率，也称为赫兹 (Hz)；每秒 200 次振荡就是 200 赫兹。
Sound waves—in fact all waves—have three fundamental characteristics: frequency, wavelength, and amplitude. Frequency is the number of waves passing a given point in a given period of time. If you are watching waves in the ocean from a boat or a cruise ship, you may notice that, say, ten waves go by in a minute, so we might say they have a frequency of ten per minute. But we actually often measure frequency in oscillations per second, also known as hertz, or Hz; 200 oscillations per second is 200 hertz.
至于波长，它指的是两个波峰之间的距离——或者也可以理解为两个波谷之间的距离。波的一个基本特性是：波的频率越高，波长越短；波长越长，频率越低。这就引出了物理学中一个极其重要的关系：波速、频率和波长之间的关系。波的波长等于其传播速度除以频率。这适用于电磁波（包括X射线、可见光、红外线和无线电波）。以及浴缸中的声波和海洋中的波浪。例如，440赫兹音调（钢琴上的中央A）在空气中的波长是340除以440，即0.77米（约30英寸）。
As for wavelength, this is the distance between two wave crests—or also between two wave valleys. One of the fundamental characteristics of waves is that the greater the frequency of a wave, the shorter its wavelength is; and the longer the wavelength, the lower its frequency. Here we’ve reached a terrifically important set of relationships in physics, those between the speed, frequency, and wavelength of waves. The wavelength of a wave is its speed divided by its frequency. This holds for electromagnetic waves (X-rays, visible light, infrared, and radio waves) as well as sound waves in a bathtub and waves in the ocean. As an example, the wavelength in air of a 440 hertz tone (middle A on the piano) is 340 divided by 440, which is 0.77 meters (about 30 inches).
仔细想想，这完全合乎逻辑。由于声速在任何介质中都是恒定的（气体除外，气体中的声速取决于温度），因此在给定时间内声波的数量越多，每个声波的波长就必须越短。反之亦然：在相同时间内声波的数量越少，每个声波的波长就必须越长。对于不同类型的波长，我们使用不同的计量单位。例如，我们用米来测量声波的波长，而用纳米来测量光的波长（一纳米等于十亿分之一米）。
If you think about this for a minute, you’ll see that it makes perfect sense. Since the speed of sound is constant in any given medium (except in gases, where it depends on temperature), the more sound waves there are in a given period of time, the shorter the waves have to be to fit into that time. And the reverse is clearly also true: the fewer the waves in the same time the longer each of them has to be. For wavelength, we have different measurements for different kinds. For example, while we measure wavelengths of sound in meters, we measure the wavelengths of light in nanometers (one nanometer is a billionth of a meter).
那么振幅呢？再想想你从船上观察海浪的情景。你会发现，即使波长相同，有些波浪的高度也比其他波浪高。波的这种特性就叫做振幅。声波的振幅决定了声音的大小：振幅越大，声音越大，反之亦然。这是因为振幅越大，波携带的能量就越多。任何冲浪者都会告诉你，海浪越高，蕴含的能量就越多。当你更用力地拨动吉他弦时，你赋予了琴弦更多的能量，从而产生了更大的声音。我们用米和厘米来测量水波的振幅。空气中声波的振幅应该是空气分子在压力波中往复运动的距离，但我们从来不用这种方式来表示。相反，我们测量的是声音的强度，用分贝来表示。分贝标度相当复杂；幸运的是，你不需要了解它。
Now what about amplitude? Think again about watching the waves out in the ocean from a boat. You will see that some waves are higher than others, even though they may have the same wavelength. This characteristic of the wave is known as its amplitude. The amplitude of a sound wave determines how loud or soft the sound will be: the greater its amplitude, the louder it is, and vice versa. This is because the larger the amplitude, the more energy a wave is carrying. As any surfer can tell you, the taller an ocean wave, the more energy it packs. When you strum guitar strings more vigorously, you are imparting more energy to them and you produce a louder sound. We measure the amplitude of water waves in meters and centimeters. The amplitude of a sound wave in air would be the distance over which the air molecules move back and forth in the pressure wave, but we never express it that way. Instead, we measure the intensity of sound, which is expressed in decibels. The decibel scale turns out to be quite complicated; fortunately, you don’t need to know about it.
声音的音高，也就是它在音阶上的位置高低，则是由频率决定的。频率越高，音高越高；频率越低，音高越低。在音乐创作中，我们不断地改变频率（从而改变音高）。
The pitch of a sound, meaning how high or low it is on the musical scale, is, on the other hand, determined by the frequency. The higher the frequency, the higher its pitch; the lower the frequency, the lower its pitch. In making music, we change the frequency (thus the pitch) all the time.
人耳能听到的频率范围非常广，从大约20赫兹（钢琴的最低音是27.5赫兹）一直到大约20,000赫兹。我在课堂上会做一个很棒的演示：我使用一台发声设备——听力计，它可以发出不同频率和强度的声音。我让学生们举手，直到他们能听到声音为止。然后我逐渐提高频率。随着年龄的增长，我们大多数人都会失去听到高频声音的能力。我自己的高频截止频率接近4,000赫兹，比中央C高四个八度，也就是钢琴键盘的最低音。但是，即使我听不到声音很久之后，我的学生们仍然能听到更高的音符。我把频率调高，一直到10,000赫兹和15,000赫兹，一些学生的手开始垂下来。到了20,000赫兹，只有大约一半的学生的手还举着。然后我放慢速度：21000、22000、23000。等到24000赫兹的时候，通常只剩下几只手举着了。这时，我会跟他们开个小玩笑：我关掉机器，但假装把频率调得更高，到27000赫兹。一两个勇敢的人声称听到了这些超高音——直到我轻轻戳破那个气球。这纯粹是开玩笑。
The human ear can hear a tremendous range of frequencies, from about 20 hertz (the lowest note on a piano is 27.5 hertz) all the way up to about 20,000 hertz. I have a great demonstration in my classes, in which I run a sound-producing machine, an audiometer, which can broadcast different frequencies and at different intensities. I ask students to hold their hands up as long as they can hear the sound. I gradually increase the frequency. When we get older, most of us lose our ability to hear high frequencies. My own high-frequency cutoff is near 4,000 hertz, four octaves above middle C, at the very end of the piano keyboard. But long after I’m hearing nothing, my students can hear much higher notes. I move the dial upward and still upward, to 10,000 and 15,000 hertz, and some hands start to drop. At 20,000 hertz, only about half of the hands are still up. Then I go more slowly: 21,000, 22,000, 23,000. By the time I get to 24,000 hertz, there are usually just a few hands still raised. At that point, I play a little joke on them; I turn the machine off but pretend to be raising the frequency even higher, to 27,000 hertz. One or two brave souls claim to be hearing these super high notes—until I gently puncture that balloon. It’s all in good fun.
现在想想音叉的工作原理。如果你用力敲击音叉，叉齿每秒振动的次数保持不变——因此它产生的声波频率也保持不变。这就是为什么它总是发出同一个音符。然而，当你用力敲击时，叉齿振动的振幅会增加。如果你拍摄敲击音叉的过程，然后慢放视频，就能看到这一点。你会看到叉齿来回摆动，敲击越用力，摆动的幅度就越大。由于振幅增大，产生的音符会更响亮，但由于叉齿的振动频率保持不变，所以音符仍然保持不变。这难道不奇怪吗？仔细想想，你会发现它和摆（第三章）的原理完全一样，摆的周期（完成一次摆动所需的时间）与摆动的振幅无关。
Now think about how a tuning fork works. If you hit a tuning fork harder, the number of vibrations per second of its prongs remains the same—so the frequency of the sound waves it produces stays the same. This is why it always plays the same note. However, the amplitude of the oscillation of its prongs does increase when you hit it harder. You could see this if you were to film the tuning fork as you hit it and then replay the film in slow motion. You would see the prongs of the fork move back and forth, and they would move farther the harder you hit them. Since the amplitude is increased, the note produced will be louder, but since the prongs continue to oscillate at the same frequency, the note stays the same. Isn’t that weird? If you think about it for a bit, you’ll see that it’s exactly like the pendulum (chapter 3), where the period (the time to complete one oscillation) is independent of the amplitude of its swings.
太空中的声波？
Sound Waves in Space?
这些关于声音的关联在地球之外也成立吗？你是否听说过太空中没有声音？这意味着无论你在月球表面多么用力地弹奏钢琴，都不会发出任何声音。这真的可能吗？是的，月球没有大气层；它基本上是一个真空。因此，你可能会得出这样的结论，或许会感到遗憾：即使是恒星或星系碰撞中最壮观的爆炸，也发生在绝对的寂静之中。我们甚至可以假设，宇宙大爆炸本身，那场大约140亿年前创造我们宇宙的原始爆炸，也是在完全寂静中发生的。但是，请稍等片刻。太空，就像生活中的许多事物一样，远比我们几十年前想象的要混乱和复杂得多。
Do these relationships of sound hold true beyond Earth? Have you ever heard that there is no sound in space? This would mean that no matter how energetically you play a piano on the surface of the Moon, it wouldn’t produce any sound. Can this be right? Yes, the Moon has no atmosphere; it is basically a vacuum. So you might conclude, perhaps sadly, that yes, even the most spectacular explosions of stars or galaxies colliding with each other occur in utter silence. We might even suppose that the big bang itself, the primordial explosion that created our universe nearly 14 billion years ago, took place entirely in silence. But hold on a minute. Space, like much of life, is considerably messier and more complicated than we thought even a few decades ago.
尽管我们任何人在太空中呼吸都会因缺氧而迅速死亡，但事实是，外太空，甚至是深空，都不是绝对真空。这些术语都是相对的。星际空间和星系际空间比我们在地球上所能制造的最佳真空环境更接近真空数百万倍。然而，事实是，漂浮在太空中的物质具有重要且可识别的特征。
Even though any of us would quickly perish from a lack of oxygen if we tried to breathe in space, the truth is that outer space, even deep space, is not a perfect vacuum. Such terms are all relative. Interstellar and intergalactic space are millions of times closer to a vacuum than the best vacuum we can make on Earth. Still, the fact is that the matter that does float around in space has important and identifiable characteristics.
宇宙中大部分物质被称为等离子体：电离气体——部分或全部由带电粒子（例如氢核（质子）和电子）组成的气体——密度差异很大。等离子体存在于我们的太阳系中，我们通常称之为太阳风，它从太阳向外喷射（布鲁诺·罗西对这一现象的研究极大地增进了我们对它的认识）。等离子体也存在于恒星内部，以及星系中恒星之间的空间（我们称之为星际介质），甚至星系之间的空间（我们称之为星系际介质）。大多数天体物理学家认为，宇宙中所有可观测物质的99.9%以上都是等离子体。
Most of this matter is called plasma: ionized gases—gases partly or completely made up of charged particles, such as hydrogen nuclei (protons) and electrons—of widely varying density. Plasma is present in our solar system, where we usually call it the solar wind, streaming outward from the Sun (the phenomenon Bruno Rossi did so much to advance our knowledge of). Plasmas are also found in stars, as well as between stars in galaxies (where we call it the interstellar medium), and even between galaxies (where we call it the intergalactic medium). Most astrophysicists believe that more than 99.9 percent of all observable matter in the universe is plasma.
想想看。凡是有物质存在的地方，就能产生压力波（也就是声音），而且压力波会传播。由于宇宙空间（包括我们的太阳系）到处都有等离子体，所以才会有如此多的声音。宇宙中存在着各种声波，尽管我们根本听不到。我们可怜的耳朵能听到相当宽广的频率范围——实际上超过三个数量级——但我们却无法听到来自天体的音乐。
Think about it. Wherever matter exists, pressure waves (thus, sound) can be produced and they will propagate. And because there are plasmas everywhere in space (also in our solar system), there are lots of sound waves out there, even though we can’t possibly hear them. Our poor ears can hear a pretty wide range of frequencies—more than three orders of magnitude, in fact—but we aren’t outfitted to hear the music of the heavenly spheres.
让我举个例子。早在2003年，物理学家们就发现，在英仙座星系团（一个距离地球约2.5亿光年的大型星系群，包含数千个星系）中，一个超大质量黑洞中心的高温气体（等离子体）周围存在涟漪。这些涟漪清晰地表明了声波的存在，这是由于黑洞吞噬物质时释放出大量能量造成的。（我将在第12章更详细地讨论黑洞。）物理学家们计算出了这些波的频率，得出的音调是降B，但这个降B的音调非常低，比中央C低57个八度（大约是中央C的10¹⁷倍），而中央C的频率约为262赫兹！您可以在http://science.nasa.gov/science-news/science-at-nasa/2003/09sep_blackholesounds/看到这些宇宙涟漪。
Let me give you one example. Back in 2003 physicists discovered ripples in the superhot gas (plasma) surrounding a supermassive black hole at the center of a galaxy in the Perseus cluster of galaxies, a large group of thousands of galaxies about 250 million light-years from Earth. These ripples clearly indicated sound waves, caused by the release of large amounts of energy when matter was swallowed up by the black hole. (I’ll get into black holes in more detail in chapter 12.) Physicists calculated the frequency of the waves and came up with a pitch of B flat, but a B flat so low that it is 57 octaves (about a factor of 1017) below middle C, whose frequency is about 262 hertz! You can see these cosmic ripples at http://science.nasa.gov/science-news/science-at-nasa/2003/09sep_blackholesounds/.
现在让我们回到宇宙大爆炸。如果孕育我们宇宙的原始爆炸在最早的物质中产生了压力波——这些物质随后膨胀、冷却，最终形成了星系、恒星，乃至行星——那么我们应该能够观测到这些声波的残余。物理学家们已经计算出早期等离子体中波纹的间距（大约50万光年）以及宇宙膨胀超过130亿年后，这些波纹的间距。他们得出的结论是，现在的间距约为5亿光年。
Now let’s go back to the big bang. If the primordial explosion that birthed our universe created pressure waves in the earliest matter—matter that then expanded and then cooled, creating galaxies, stars, and eventually planets—then we ought to be able to see the remnants of those sound waves. Well, physicists have calculated how far apart the ripples in the early plasma should have been (about 500,000 light-years) and how far apart they should be now, after the universe has been expanding for more than 13 billion years. The distance they came up with is about 500 million light-years.
目前有两个规模庞大的星系测绘项目正在进行中——新墨西哥州的斯隆数字巡天（SDSS）和澳大利亚的两度视场（2dF）星系红移巡天。这两个项目都在寻找星系分布中的这种波动，并且各自独立地发现了……你猜怎么着？他们发现“星系之间目前最有可能相距5亿光年，而不是其他任何距离”。也就是说，宇宙大爆炸产生的低音钟声，其波长约为5亿光年，频率约为5000次方米/秒。比我们耳朵能听到的任何声音低八度（ 10¹⁵倍）。天文学家马克·惠特尔（Mark Whittle）一直在研究他所谓的“大爆炸声学”，你也可以通过访问他的网站www.astro.virginia.edu/~dmw8f/BBA_web/index_frames.html来体验一番。在这个网站上，你可以看到并听到他是如何同时压缩时间（将 1 亿年压缩成 10 秒）并将早期宇宙的音调人为地提高 50 个八度，从而聆听大爆炸产生的“音乐”。
There are two enormous galaxy-mapping projects going on right now—the Sloan Digital Sky Survey (SDSS) in New Mexico and the Two-degree Field (2dF) Galaxy Redshift Survey in Australia. They have both looked for these ripples in the distribution of galaxies and have independently found… guess what? They found “that galaxies are currently slightly more likely to be 500 million light-years apart than any other distance.” So the big bang produced a bass gong sound that now has a wavelength of about 500 million light-years, a frequency about fifty octaves (a factor of 1015) below anything our ears can hear. The astronomer Mark Whittle has played around a good bit with what he calls big bang acoustics, and you can too, by accessing his website: www.astro.virginia.edu/~dmw8f/BBA_web/index_frames.html. On the site, you can see and hear how he has simultaneously compressed time (turning 100 million years into 10 seconds) and artificially raised the pitch of the early universe fifty octaves, so you can listen to the “music” created by the big bang.
共鸣的奇妙之处
The Wonders of Resonance
我们称之为共振的现象，使得许多事物成为可能，而如果没有共振，这些事物要么根本不可能存在，要么就会逊色很多：不仅是音乐，还有收音机、手表、蹦床、游乐场秋千、电脑、火车汽笛、教堂钟声，以及你可能在膝盖或肩膀上做过的核磁共振成像（你知道“R”代表“共振”吗？）。
The phenomenon we call resonance makes a huge number of things possible that either could not exist at all or would be a whole lot less interesting without it: not only music, but radios, watches, trampolines, playground swings, computers, train whistles, church bells, and the MRI you may have gotten on your knee or shoulder (did you know that the “R” stands for “resonance”?).
共振究竟是什么？你可以想象一下推孩子荡秋千的情景来更好地理解它。你凭直觉就知道，只需很小的力气就能让秋千摆动得很大。因为秋千（它本质上是一个钟摆）有一个固定的频率（见第三章），如果你能精准地把握推秋千的时机，使之与这个频率同步，那么即使是微小的额外推力也能对秋千的摆动幅度产生巨大的累积影响。你只需用两根手指轻轻一推，就能让孩子荡得越来越高。
What exactly is resonance? You can get a good feeling for this by thinking of pushing a child on a swing. You know, intuitively, that you can produce large amplitudes of the swing with very little effort. Because the swing, which is a pendulum, has a uniquely defined frequency (chapter 3), if you accurately time your pushes to be in sync with that frequency, small amounts of additional push have a large cumulative impact on how high the swing goes. You can push your child higher and higher with just light touches of only a couple of fingers.
这样做，你就是在利用共振。在物理学中，共振是指物体（无论是摆锤、音叉、小提琴弦、酒杯、鼓皮、钢梁、原子、电子、原子核，甚至是空气柱）在某些频率下振动比其他频率下振动更强烈的现象。这些频率我们称之为共振频率（或固有频率）。
When you do this, you are taking advantage of resonance. Resonance, in physics, is the tendency of something—whether a pendulum, a tuning fork, a violin string, a wineglass, a drum skin, a steel beam, an atom, an electron, a nucleus, or even a column of air—to vibrate more powerfully at certain frequencies than at others. These we call resonance frequencies (or natural frequencies).
例如，音叉的构造使其始终以其共振频率振动。如果它以 440 赫兹的频率振动，那么它发出的就是已知的音符。它就像钢琴上中央C上方的A音一样。无论你用什么方法让它振动，它的金属臂都会以每秒440次的频率往复振动。
A tuning fork, for instance, is constructed to always vibrate at its resonance frequency. If it does so at 440 hertz, then it makes the note known as concert A, the A above middle C on the piano. Pretty much no matter how you get it vibrating, its prongs will oscillate, or move back and forth, 440 times per second.
所有材料都有共振频率。如果你给一个系统或物体施加能量，它可能会开始以这些频率振动。在这些频率下，只需相对较小的能量输入就能产生非常显著的效果。例如，当你用勺子轻轻敲击一个精致的空酒杯，或者用湿手指摩擦杯沿时，它会发出特定的音调——这就是共振频率。共振并非免费的午餐，尽管有时看起来像。但在共振频率下，物体能最有效地利用你输入的能量。
All materials have resonance frequencies, and if you can add energy to a system or an object it may start to vibrate at these frequencies, where it takes relatively little energy input to have a very significant result. When you tap a delicate empty wineglass gently with a spoon, for example, or rub the rim with a wet finger, it will ring with a particular tone—that is a resonance frequency. Resonance is not a free lunch, though at times it looks like one. But at resonance frequencies, objects make the most efficient use of the energy you put into them.
跳绳的原理也一样。如果你曾经握过绳子的一端，就会知道需要一段时间才能让绳子摆动出一个漂亮的弧线——虽然你可能用手绕着绳子转圈来获得这个弧线，但这个动作的关键在于你要上下或前后摆动，使绳子振动。当达到某个阶段，绳子就会欢快地摆动出一个优美的弧线；你几乎不需要移动手就能让它保持摆动，你的朋友们就可以在弧线中间开始跳跃，凭直觉就能根据绳子的共振频率来调整跳跃的节奏。
A jump rope works on the same principle. If you’ve ever held one end, you know that it takes a while to get the rope swinging in a nice arc—and while you may have circled your hand around with the end to get that arc, the key part of that motion is that you are going up and down or back and forth, oscillating the rope. At a certain point, the rope starts swinging around happily in a beautiful arc; you barely have to move your hand to keep it going, and your friends can start jumping in the middle of the arc, intuitively timing their jumps to the resonant frequency of the rope.
你可能在操场上没注意到，跳绳只需要一个人挥动手——另一个人只需抓住绳子的另一端，就能顺利进行。关键在于，你们两人共同作用，达到了绳子的最低共振频率，也就是基频。如果没有这个原理，我们熟知的双人跳绳游戏——两个人分别向相反方向挥动两根绳子——几乎是不可能的。之所以两根绳子能够向相反方向运动，并且由同一个人握住，是因为每根绳子维持运动所需的能量都非常小。由于你的双手是驱动力，跳绳就变成了我们所说的受迫振荡器。你凭直觉就知道，一旦达到绳子的共振频率，就应该保持在这个频率，所以不要再加快挥动手的速度。
You may not have known this on the playground, but only one person has to move her hand—the other one can simply hold on to the other end, and it works just fine. The key is that between the two of you, you’ve reached the rope’s lowest resonance frequency, also called the fundamental. If it weren’t for this, the game we know as double-dutch, in which two people swing two ropes in opposite directions, would be just about impossible. What makes it possible for two ropes to be going in opposite directions, and be held by the same people, is that each one requires very little energy to keep it going. Since your hands are the driving force here, the jump rope becomes what we call a driven oscillator. You know, intuitively, once you reach this resonance of the rope, that you want to stay at that frequency, so you don’t move your hand any faster.
如果你那样做，原本优美的旋转弧线就会变成绳子乱扭，跳绳者很快就会感到烦躁。但如果你有一根足够长的绳子，并且能够更快地振动绳子的一端，你会发现绳子很快就会形成两个弧线，一个向下，一个向上，而绳子的中点则保持静止。我们称这个中点为节点。在这个节点上，你的两个朋友可以分别在两个弧线上跳跃。你可能在马戏团里见过这种现象。这是怎么回事呢？你已经达到了第二个共振频率。几乎所有能够振动的物体都有多个共振频率，我稍后会详细解释。你的跳绳也有更高的共振频率，我可以向你展示。
If you did, the beautiful rotating arc would break up into rope squiggles, and the jumper would quickly get annoyed. But if you had a long enough rope, and could vibrate your end more quickly, you would find that pretty soon the rope would create two arcs, one going down while the other went up, and the midpoint of the rope would stay stationary. We call that midpoint a node. At that point two of your friends could jump, one in each arc. You may have seen this in circuses. What is going on here? You have achieved a second resonance frequency. Just about everything that can vibrate has multiple resonance frequencies, which I’ll discuss more in just a minute. Your jump rope has higher resonance frequencies too, which I can show you.
我在课堂上用跳绳来演示多种共振频率。我将一根大约十英尺长的绳子悬挂在两根垂直的杆子之间。当我上下移动绳子的一端（大约一英寸左右），使其在杆子上振动时（使用一个可以调节频率的小马达），绳子很快就会达到最低共振频率，我们称之为基频（也称为一次谐波），并像跳绳一样划出一道弧线。当我加快绳子振动的速度时，我们很快就会看到两道互为镜像的弧线。我们称之为二次谐波，当绳子振动的频率是基频的两倍时，就会出现二次谐波。例如，如果基频是2赫兹，即每秒振动两次，那么二次谐波就是4赫兹。如果我们继续加快振动速度，当频率达到基频的三倍，也就是6赫兹时，就会出现三次谐波。我们可以看到绳子被均分为三段，绳子上的两个点（节点）不会移动，随着绳子末端每秒上下移动六次，弧线交替上下运动。
I use a jump rope to show multiple resonance frequencies in my class by suspending a single rope, about ten feet long, between two vertical rods. When I move one end of the rope up and down (only an inch or so), oscillating it on a rod, using a little motor whose frequency I can change, soon it will hit its lowest resonance frequency, which we call the first harmonic (it is also called the fundamental), and make one arc like the jump rope. When I oscillate the end of the rope more rapidly, we soon see two arcs, mirror images of each other. We call this the second harmonic, and it will come when we are oscillating the string at twice the rate of the first harmonic. So if the first harmonic is at 2 hertz, two vibrations per second, the second is at 4 hertz. If we oscillate the end still faster, when we reach three times the frequency of the first harmonic, in this case 6 hertz, we’ll reach the third harmonic. We see the string divide equally into thirds with two points of the string (nodes) that do not move, with the arcs alternating up and down as the end goes up and down six times per second.
还记得我说过我们能听到的最低音大约是20赫兹吗？这就是为什么你听不到操场跳绳发出的任何声音——它的频率太低了。但如果我们用另一种弦——比如说小提琴或大提琴上的弦——就会发生完全不同的情况。就拿小提琴来说吧。相信我，你肯定不想让我拉——我这六十年来琴技一点进步都没有。
Remember I said that the lowest note we can hear is about 20 hertz? That’s why you don’t hear any music from a playground jump rope—its frequency is way too low. But if we play with a different kind of string—one on a violin or cello, say—something else entirely happens. Take a violin. You don’t want me to take it, believe me—I haven’t improved in the past sixty years.
为了让你在小提琴上听到悠长、优美、哀婉的音符，背后已经发生了大量的物理现象。小提琴、大提琴、竖琴、吉他弦——任何弦或绳——的声音都取决于三个因素：长度、张力和重量。弦越长，张力越低；弦越重，音调越低。反之亦然：弦越短，张力越高；弦越轻，音调越高。弦乐演奏者每次演奏一段时间后，都需要调整琴弦的张力，才能发出正确的频率，也就是音符。
In order for you to hear one long, beautiful, mournful note on a violin, there’s an enormous amount of physics that has already happened. The sound of a violin, or cello, or harp, or guitar string—of any string or rope—depends on three factors: its length, its tension, and its weight. The longer the string, the lower the tension, and the heavier the string, the lower the pitch. And, of course, the converse: the shorter the string, the higher the tension, and the lighter the string, the higher the pitch. Whenever string musicians pick up their instruments after a while, they have to adjust the tension of their strings so they will produce the right frequencies, or notes.
但神奇之处在于，当小提琴家用琴弓摩擦琴弦时，她将能量传递给了琴弦，琴弦会以某种方式（从所有可能的振动频率中）选择出自身的共振频率，而且——更令人惊奇的是——即使我们看不到，它也会同时以几种不同的共振频率（多个谐波）振动。这与音叉不同，音叉只能以单一频率振动。
But here’s the magic. When the violinist rubs the string with a bow, she is imparting energy to the string, which somehow picks out its own resonance frequencies (from all the vibrations possible), and—here’s the even more mind-blowing part—even though we cannot see it, it vibrates simultaneously in several different resonance frequencies (several harmonics). It’s not like a tuning fork, which can only vibrate at a single frequency.
这些额外的谐波（频率高于基频）通常被称为泛音。各种共振频率相互作用，有的强，有的弱——这种谐波组合——赋予了小提琴或大提琴的音符以专业术语中的“音色”或“音质”，而我们则将其视为独特的音色。这正是音叉、听力计或无线电紧急广播的单一频率所发出的声音与乐器更为复杂的声音之间的区别，乐器同时以多个谐波频率振动。小号、双簧管、班卓琴、钢琴或小提琴的独特音色都源于每种乐器产生的独特谐波组合。我喜欢想象一位隐形的宇宙调酒师，他精通调制数百种不同的谐波组合，可以给这位顾客上班卓琴，给下一位上定音鼓，再给下一位上二胡或长号。
These additional harmonics (with frequencies higher than the fundamental) are often called overtones. The interplay of the varied resonant frequencies, some stronger, some weaker—the cocktail of harmonics—is what gives a violin or cello note what is known technically as its color or timbre, but what we recognize as its distinctive sound. That’s the difference between the sound made by the single frequency of the tuning fork or audiometer or emergency broadcast message on the radio and the far more complex sound of musical instruments, which vibrate at several harmonic frequencies simultaneously. The characteristic sounds of a trumpet, oboe, banjo, piano, or violin are due to the distinct cocktail of harmonic frequencies that each instrument produces. I love the image of an invisible cosmic bartender, expert in creating hundreds of different harmonic cocktails, who can serve up a banjo to this customer, a kettledrum to the next, and an erhu or a trombone to the one after that.
那些发明了第一批乐器的人，巧妙地创造了乐器的另一个重要特征，使我们能够享受音乐。它们的声音。为了听到音乐，声波不仅必须在人耳可听见的频率范围内，而且音量也必须足够大。例如，仅仅拨动琴弦并不能产生足够大的声音，以至于远处的人听不到。你可以通过更用力地拨动琴弦来赋予它更多的能量（从而增强它产生的声波），但你仍然可能无法发出非常洪亮的声音。幸运的是，早在很久以前，至少几千年前，人类就找到了让弦乐器发出足够大的声音的方法，这样就能在空地或房间里听到它们的声音了。
Those who developed the first musical instruments were ingenious in crafting another vital feature of instruments that allows us to enjoy their sound. In order to hear music, the sound waves not only have to be within the frequency range you can hear, but they also must be loud enough for you to hear them. Simply plucking a string, for instance, doesn’t produce enough sound to be heard at a distance. You can impart more energy to a string (and hence to the sound waves it produces) by plucking it harder, but you still may not produce a very robust sound. Fortunately, a great many years ago, millennia at least, human beings figured out how to make string instruments loud enough to be heard across a clearing or room.
你可以重现我们祖先面临的难题——然后解决它。拿一根一英尺长的绳子，一端系在门把手或抽屉把手上，拉紧另一端，然后用另一只手拨动它。没什么特别的，对吧？你能听到声音，而且根据绳子的长度、粗细和拉紧的程度，你或许能发出一个可以辨认的音符。但声音很小，对吧？隔壁房间的人根本听不见。现在，如果你拿一个塑料杯，把绳子穿过杯子，把绳子举起来，使其与门把手或把手保持一定角度（这样它就不会滑向你的手），然后拨动绳子，你会听到更大的声音。为什么呢？因为绳子会将一部分能量传递给杯子，杯子现在以相同的频率振动，只是它的表面积更大，可以将振动传递给空气。结果，你听到的声音就更大了。
You can reproduce the precise problem our ancestors faced—and then solve it. Take a foot-long piece of string, tie one end to a doorknob or drawer handle, pull on the other end until it’s tight, and then pluck it with your other hand. Not much happens, right? You can hear it, and depending on the length of the string, how thick it is, and how tight you hold it, you might be able to make a recognizable note. But the sound isn’t very strong, right? No one would hear it in the next room. Now, if you take a plastic cup and run the string through the cup, hold the string up at an angle away from the knob or handle (so it doesn’t slide toward your hand), and pluck the string, you’ll hear more sound. Why? Because the string transmits some of its energy to the cup, which now vibrates at the same frequency, only it’s got a much larger surface area through which to impart its vibrations to the air. As a result, you hear louder sound.
你用杯子演示了共鸣板的原理——这对于所有弦乐器都至关重要，从吉他、低音提琴到小提琴和钢琴。共鸣板通常由木头制成，它能拾取琴弦的振动并将这些频率传递到空气中，从而大大放大琴弦的声音。
With your cup you have demonstrated the principle of a sounding board—which is absolutely essential to all stringed instruments, from guitars and bass fiddles to violins and the piano. They’re usually made of wood, and they pick up the vibrations of the strings and transmit these frequencies to the air, greatly amplifying the sound of the strings.
吉他和提琴的音板很容易看到。三角钢琴的音板是平的、水平的，位于琴弦下方，琴弦就安装在音板上；立式钢琴的音板则垂直于琴弦后方。竖琴的音板通常是琴弦固定的底座。
The sounding boards are easy to see in guitars and violins. On a grand piano, the sounding board is flat, horizontal, and located underneath the strings, which are mounted on the sounding board; it stands vertically behind the strings on an upright. On a harp, the sounding board is usually the base where the strings are attached.
在课堂上，我用不同的方法演示音板的工作原理。其中一个演示是用我女儿艾玛在幼儿园做的乐器。它其实就是一根普通的绳子，系在一个肯德基的纸盒上。你可以用一块木头来调节绳子的张力。这真的很有趣；我增加张力，音调就升高。肯德基的纸盒就是一个完美的音板，我的学生们在很远的地方都能听到拨弦的声音。另一个我最喜欢的演示是用一个我多年前在奥地利买的音乐盒；它比火柴盒还小，而且没有音板。当你转动曲柄时，它会通过振动的金属片发出音乐。我在课堂上转动曲柄，没有人能听到，连我自己也听不到！然后我把它放在我的实验台上，再转动一次曲柄。现在所有的学生都能听到了，即使是坐在大讲堂后排的学生也能听到。即使是这么简单的音板也能如此有效，这总是让我感到惊讶。
In class I demonstrate the workings of a sounding board in different ways. In one demonstration I use a musical instrument my daughter Emma made in kindergarten. It’s one ordinary string attached to a Kentucky Fried Chicken cardboard box. You can change the tension in the string using a piece of wood. It’s really great fun; as I increase the tension the pitch goes up. The KFC box is a perfect sounding board, and my students can hear the plucking of the string from quite far away. Another one of my favorite demos is with a music box that I bought many years ago in Austria; it’s no bigger than a matchbox and it has no sounding board attached to it. When you turn the crank, it makes music produced by vibrating prongs. I turn the crank in class and no one can hear it, not even I! Then I place it on my lab table and turn the crank again. All the students can now hear it, even those way in the back of my large lecture hall. It always amazes me how very effective even a very simple sounding board can be.
但这并不意味着它们有时就不是真正的艺术品。制造高品质乐器有很多秘诀，斯坦威父子公司不太可能告诉你他们是如何制作举世闻名的钢琴的音板的！你可能听说过十七、十八世纪著名的斯特拉迪瓦里家族，他们制作了最精美绝伦、最令人梦寐以求的小提琴。据知，斯特拉迪瓦里小提琴仅存约540把；其中一把在2006年以350万美元的价格售出。一些物理学家对这些小提琴进行了广泛的研究，试图揭开“斯特拉迪瓦里秘密”，希望能够制造出音色同样美妙、价格低廉的小提琴。你可以在www.sciencedaily.com/releases/2009/01/090122141228.htm上阅读一些相关研究。
That doesn’t mean that they’re not sometimes works of real art. There is a lot of secrecy about building high-quality musical instruments, and Steinway & Sons are not likely to tell you how they build the sounding boards of their world-famous pianos! You may have heard of the famous Stradivarius family in the seventeenth and eighteenth centuries who built the most fantastic and most desirable violins. Only about 540 Stradivarius violins are known to exist; one was sold in 2006 for $3.5 million. Several physicists have done extensive research on these violins in an effort to uncover the “Stradivarius secrets” in the hope that they would be able to build cheap violins with the same magic voice. You can read about some of this research at www.sciencedaily.com/releases/2009/01/090122141228.htm.
某些音符组合听起来悦耳或不悦耳，很大程度上取决于它们的频率和泛音。在西方音乐中，最常见的音符组合是频率正好是另一个音符两倍的组合。我们称这些音符相隔一个八度。但还有许多其他悦耳的组合：和弦、三度、五度等等。
A good deal of what makes certain combinations of notes sound more or less pleasing to us has to do with frequencies and harmonics. The best-known type of note pairing, at least in Western music, is of notes where one is exactly twice the frequency of the other. We say that these notes are separated by an octave. But there are many other pleasing combinations as well: chords, thirds, fifths, and so on.
自古希腊毕达哥拉斯时代起，数学家和“自然哲学家”就对不同频率之间优美的数字关系着迷。历史学家们对于毕达哥拉斯究竟发现了多少，借鉴了多少巴比伦人的知识，以及他的追随者又发现了多少，莫衷一是。但人们普遍认为，毕达哥拉斯发现了不同长度和张力的弦会以可预测且悦耳的比例产生不同的音高。许多物理学家乐于称他为第一位弦理论家。
Mathematicians and “natural philosophers” have been fascinated by the beautiful numerical relationships between different frequencies since the time of Pythagoras in ancient Greece. Historians disagree over just how much Pythagoras figured out, how much he borrowed from the Babylonians, and how much his followers discovered, but he seems to get the credit for figuring out that strings of different lengths and tensions produce different pitches in predictable and pleasing ratios. Many physicists delight in calling him the very first string theorist.
乐器制造者巧妙地运用了这一原理。例如，小提琴上的每根琴弦都具有不同的重量和张力，即使长度大致相同，也能产生不同频率和泛音。小提琴演奏者通过在琴颈上上下移动手指来改变琴弦的长度。当手指靠近下巴时，会缩短琴弦的长度，从而提高第一泛音以及所有更高泛音的频率（即音高）。这其中的原理相当复杂。一些弦乐器，例如印度西塔琴，拥有所谓的共鸣弦，这些额外的琴弦位于演奏弦的旁边或下方，当乐器演奏时，它们会以自身的共振频率振动。
Instrument makers have made brilliant use of this knowledge. The different strings on a violin, for example, all have different weights and tensions, which enable them to produce higher and lower frequencies and harmonics even though they all have about the same length. Violinists change the length of their strings by moving their fingers up and down the violin neck. When their fingers walk toward their chins, they shorten the length of any given string, increasing the frequency (thus the pitch) of the first harmonic as well as all the higher harmonics. This can get quite complex. Some stringed instruments, like the Indian sitar, have what are called sympathetic strings, extra strings alongside or underneath the playing strings that vibrate at their own resonance frequencies when the instrument is being played.
要直接观察乐器琴弦上的多种谐波频率几乎是不可能的，但我可以通过将麦克风连接到示波器来直观地展示它们。你可能在电视上见过示波器，即使没亲眼见过。示波器会在屏幕上显示振动（或振荡）随时间的变化，表现为一条在中心水平线上下波动的曲线。重症监护室和急诊室里到处都是示波器，用来测量病人的心跳。
It’s difficult if not impossible to see the multiple harmonic frequencies on the strings of an instrument, but I can show them dramatically by connecting a microphone to an oscilloscope, which you have probably seen on TV, if not in person. An oscilloscope shows a vibration—or oscillation—over time, on a screen, in the form of a line going up and down, above and below a central horizontal line. Intensive care units and emergency rooms are filled with them for measuring patients’ heartbeats.
我总是邀请我的学生把他们的乐器带到课堂上，这样我们就可以看到每种乐器产生的各种和声组合。
I always invite my students to bring their musical instruments to class so that we can see the various cocktails of harmonics that each produces.
当我把音叉（A调）举到麦克风前时，屏幕上会显示一条简单的440赫兹正弦曲线。这条曲线干净且极其规则，因为正如我们所见，音叉产生的频率恰好为440赫兹。只有一个频率。但当我邀请一位带着小提琴的学生来演奏同样的A音时，屏幕上的波形就变得有趣多了。基频依然存在——你可以在屏幕上看到它，它表现为一条主要的正弦曲线——但由于高次谐波的存在，这条曲线变得更加复杂。而当一位学生演奏大提琴时，情况又有所不同。想象一下，如果一位小提琴手同时演奏两个音符会发生什么！
When I hold a tuning fork for concert A up to the microphone, the screen shows a simple sine curve of 440 hertz. The line is clean and extremely regular because, as we’ve seen, the tuning fork produces just one frequency. But when I invite a student who brought her violin to play the same A, the screen gets a whole lot more interesting. The fundamental is still there—you can see it on the screen as the dominant sine curve—but the curve is now much more complex due to the higher harmonics, and it’s different again when a student plays his cello. Imagine what happens when a violinist plays two notes at once!
当歌手通过声带（“声襞”或许是更准确的描述）振动空气来展现共鸣的物理原理时，声带膜会振动并产生声波。我让一位学生也唱歌，示波器也显示了同样的现象，屏幕上叠加着同样复杂的曲线。
When singers start demonstrating the physics of resonance by sending air through their vocal cords (“vocal folds” would be a more descriptive term), membranes vibrate and create sound waves. I ask a student to sing too, and the oscilloscope tells the same story, as similarly complicated curves pile up on the screen.
弹钢琴时，你按下的琴键会使琴槌敲击琴弦——一根金属丝——琴弦的长度、重量和张力都经过设定，使其以特定的基频振动。但不知何故，就像小提琴弦和声带一样，钢琴弦也会同时以更高的谐波振动。
When you play the piano, the key that you press makes a hammer hit a string—a wire—whose length, weight, and tension have been set to oscillate at a given first harmonic frequency. But somehow, just like violin strings and vocal cords, the piano strings also vibrate simultaneously at higher harmonics.
现在，让我们进行一次大胆的思维飞跃，进入亚原子世界，想象一下那些比原子核小得多、如同小提琴般微小的弦，它们以不同的频率和不同的谐波振动。换句话说，设想一下，构成物质的基本单元或许就是这些微小的振动弦，它们通过在不同的谐波频率和多个维度上振动，产生所有所谓的基本粒子——例如夸克、胶子、中微子和电子。如果你已经完成了这一步，那么你就已经掌握了弦理论的基本命题。弦理论是过去四十年来理论物理学家们为构建一个能够解释宇宙中所有基本粒子和所有力的单一理论而做出的努力的总称。从某种意义上说，它是一个“万物理论”。
Now take a tremendous thought-leap into the subatomic world and imagine super-tiny violinlike strings, much, much smaller than an atomic nucleus, that oscillate at different frequencies and different harmonics. In other words, consider the possibility that the fundamental building blocks of matter are these tiny vibrating strings, which produce all the so-called elementary particles—such as quarks, gluons, neutrinos, electrons—by vibrating at different harmonic frequencies, and in many dimensions. If you’ve managed to take this step, you’ve just grasped the fundamental proposition of string theory, the catchall term to describe the efforts of theoretical physicists over the past forty years to come up with a single theory accounting for all elementary particles and all the forces in the universe. In a way, it’s a theory of “everything.”
没人知道弦理论能否成功，诺贝尔奖得主谢尔顿·格拉肖也曾质疑它究竟是“物理学理论还是哲学理论”。但如果宇宙最基本的单元真的是难以想象的微小弦的不同共振频率，那么宇宙及其力和基本粒子或许会与此类似。这是莫扎特对《一闪一闪小星星》精彩而又日益复杂的变奏曲的宇宙版本。
No one has the slightest idea whether string theory will succeed, and the Nobel laureate Sheldon Glashow has wondered whether it’s “a theory of physics or a philosophy.” But if it’s true that the most basic units of the universe are the different resonance levels of unimaginably tiny strings, then the universe, and its forces and elementary particles, may resemble a cosmic version of Mozart’s wonderful, increasingly complex variations on “Twinkle, Twinkle Little Star.”
所有物体都有共振频率，从冰箱里的番茄酱瓶到世界最高建筑，无一例外；许多共振频率神秘莫测，难以预测。如果你有车，肯定听过共振声，而且肯定不是什么令人愉快的声音。你肯定有过这样的经历：开车时听到某种噪音，然后随着车速加快，噪音就消失了。
All objects have resonant frequencies, from the bottle of ketchup in your refrigerator to the tallest building in the world; many are mysterious and very hard to predict. If you have a car, you’ve heard resonances, and they didn’t make you happy. Surely you’ve had the experience of hearing a noise while driving, and hearing it disappear when you go faster.
我的上一辆车，每次等红灯怠速时，仪表盘似乎都会发出某种共振频率。如果我踩油门，即使车子没动，发动机转速提高，也能改变车身振动的频率，噪音就消失了。有时候，我会听到一种新的噪音，持续一段时间，但通常开快点或慢点就又会消失。在不同的车速下，也就是不同的振动频率下，这辆车——以及它成千上万个零件（唉，其中一些已经松动了）——会达到共振频率，比如松动的消音器或老化的发动机支架，然后它们就会发出“警报”。它们都在说同样的话——“把我送到修理厂去；把我送到修理厂去”——但我常常置之不理，直到后来才发现这些共振造成的损害。当我最终把车送去修理时，我却无法重现那些可怕的噪音，感觉自己真是太蠢了。
On my last car the dashboard seemed to hit its fundamental frequency whenever I idled at a traffic light. If I hit the gas, speeding up the engine, even if I wasn’t moving, I changed the frequency of the car’s vibrations, and the noise disappeared. Sometimes I would hear a new noise for a while, which usually went away when I drove faster or slower. At different speeds, which is to say different vibrating frequencies, the car—and its thousands of parts, some of which were loose, alas—hit a resonant frequency of, say, its loose muffler or deteriorating motor mounts, and they talked to me. They all said the same thing—“Take me to the mechanic; take me to the mechanic”—which I too often ignored, only to discover later the damage that these resonances had done. When I finally took the car in, I could not reproduce the awful sounds and I felt kind of stupid.
我记得学生时代，我们兄弟会请了一位我们不喜欢的晚宴演讲嘉宾，我们就拿出酒杯，用湿手指沿着杯沿划一圈——这在家也能轻松做到——发出一种声音。这就是我们酒杯的基频。一百个学生同时这么做的时候，确实很烦人（毕竟这是兄弟会嘛）——但效果也非常好，演讲嘉宾最终明白了我们的意思。
I remember when I was a student, when we had an after-dinner speaker in my fraternity we didn’t like, we would take our wineglasses and run our wet fingers around the rim, something you can do at home easily, and generate a sound. This was the fundamental frequency of our wineglasses. When we got a hundred students doing it at once, it was very annoying, to be sure (this was a fraternity, after all)—but it was also very effective, and the speakers got the message.
大家都听说过，歌剧演员只要唱对音调，声音足够大，就能震碎酒杯。既然你了解了共振，这怎么可能呢？理论上很简单，对吧？如果你拿一个酒杯，测量它的基频，然后发出一个相同频率的声音，会发生什么呢？嗯，就我的经验而言，大多数情况下，什么都不会发生。我从未见过歌剧演员这样做。因此，我的课堂上不用歌剧演员。我选择一个酒杯，轻敲几下，用示波器测量它的基频——当然，每个酒杯的基频都不一样，但我用的酒杯的基频总是在440到480赫兹之间。然后，我用电子设备生成一个与酒杯基频完全相同的声音（当然，完全一致是不可能的，但我会尽量接近）。我把它连接到放大器上，然后慢慢调大音量。为什么要调大音量呢？因为声音越大，声波的能量就越大，撞击到酒杯上的能量也就越多。酒杯振动的振幅越大，酒杯的弯曲程度就越大，直到它破碎（我们希望如此）。
Everyone has heard that an opera singer singing the right note loud enough can break a wineglass. Now that you know about resonance, how could that happen? It’s simple, at least in theory, right? If you took a wineglass, measured the frequency of its fundamental, and then generated a sound at that frequency, what would happen? Well, most of the time, in my experience, nothing at all. I’ve never seen an opera singer do it. I therefore don’t use an opera singer in my class. I select a wineglass, tap on it, and measure its fundamental frequency with an oscilloscope—of course it varies from glass to glass, but for the glasses I use it’s always somewhere in the range of 440 to 480 hertz. I then generate electronically a sound with the exact same frequency of the fundamental of the wineglass (well exact, of course, is never possible, but I try to get very close). I connect it to an amplifier, and slowly crank up the volume. Why increase the volume? Because the louder the sound, the more energy in the sound wave will be beating against the glass. And the greater the amplitude of the vibrations in the wineglass, the more and more the glass will bend in and out, until it breaks (we hope).
为了展示玻璃的振动，我用相机放大拍摄，并用频闪灯照射它，频闪灯的频率与声音的频率略有不同。效果太棒了！你可以看到酒杯的杯身开始振动；杯身两侧先是收缩，然后分开，随着我提高扬声器的音量，它们之间的距离越来越大，有时我需要稍微调整一下频率，然后——砰！ ——玻璃就碎了。这总是学生们最喜欢的部分；他们迫不及待地想看到玻璃破碎。（你可以在我的电磁学课程8.02版第27讲中看到这段视频，大约在6分钟左右，网址是：http: //ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-27-resonance-and-destructive-resonance/。）
In order to show the glass vibrating, I zoom in on it with a camera and illuminate it with a strobe light, set to a slightly different frequency than the sound. It’s fantastic! You see the bowl of the wineglass beginning to vibrate; the two opposite sides first contract, then push apart, and the distance they move grows and grows as I increase the volume of the speaker, and sometimes I have to tweak the frequency slightly and then—poof!—the glass shatters. That’s always the best part for the students; they can’t wait for the glass to break. (You can see this online about six minutes into lecture 27 of my Electricity and Magnetism course, 8.02, at: http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-27-resonance-and-destructive-resonance/.)
我还喜欢向学生们展示一种叫做克拉尼板的装置，它能以最奇特、最美妙的方式展现共振效应。这些金属板直径约一英尺，可以是正方形、长方形，甚至是圆形，但正方形的效果最佳。它们被固定在一根杆子或底座上，中心点朝下。我们在金属板上撒上一些细粉，然后用小提琴弓沿着金属板的一侧摩擦，摩擦的长度要覆盖整个弓身。金属板会开始在其一个或多个共振频率上振动。在金属板振动波的波峰和波谷处，粉末会脱落，露出裸露的金属；粉末则会积聚在波节处，也就是金属板完全不振动的地方。（琴弦也有波节。）点，但二维物体，例如克拉迪尼板，则有节点线。）
I also love to show students something called Chladni plates, which demonstrate, in the oddest and most beautiful ways, the effects of resonance. These metal plates are about a foot across, and they can be square, rectangular, or even circular, but the best are square. They are fastened to a rod or a base at their centers. We sprinkle some fine powder on the plate and then rub a violin bow along one of the sides, the whole length of the bow. The plate will start to oscillate in one or more of its resonance frequencies. At the peaks and valleys of the vibrating waves on the plate, the powder will shake off and leave bare metal; it will accumulate at the nodes, where the plate does not vibrate at all. (Strings have nodal points, but two-dimensional objects, like the Chladini plate, have nodal lines.)
根据你用琴弓摩擦金属板的方式和位置，你会激发不同的共振频率，并在其表面形成奇妙且完全无法预测的图案。在课堂上，我使用一种更高效——但远不如前者浪漫——的技巧，将金属板连接到振动器上。通过改变振动器的频率，我们可以看到最引人注目的图案出现和消失。你可以在YouTube上看到我所说的：www.youtube.com/watch ?v=6wmFAwqQB0g。试着想象一下这些图案背后的数学原理吧！
Depending on how and where you “play” the plate by rubbing it with the bow, you will excite different resonance frequencies and make amazing, completely unpredictable patterns on its surface. In class I use a more efficient—but far less romantic—technique and hook the plate up to a vibrator. By changing the frequency of the vibrator, we see the most remarkable patterns come and go. You can see what I mean here, on YouTube: www.youtube.com/watch?v=6wmFAwqQB0g. Just try to imagine the math behind these patterns!
在我为儿童和家庭举办的公开讲座中，我会邀请孩子们用弓弦摩擦盘子边缘——他们很喜欢创造出如此美丽而神秘的图案。这就是我想通过物理学向大家传达的理念。
In the public lectures I do for kids and families, I invite the little ones to rub the plate edges with the bow—they love making such beautiful and mysterious patterns. That’s what I’m trying to get across about physics.
风的音乐
The Music of the Winds
但我们漏掉了半个管弦乐队！长笛、双簧管或长号怎么样？毕竟，它们没有琴弦振动，也没有音板来发声。尽管它们历史悠久——不久前我在报纸上看到一张用秃鹫骨雕刻而成的、距今35000年的长笛照片——但管乐器比弦乐器更神秘一些，部分原因是它们的机械结构是不可见的。
But we’ve left out half the orchestra! How about a flute or oboe or trombone? After all, they don’t have a string to vibrate, or a soundboard to project their sound. Even though they are ancient—I saw a photograph of a 35,000-year-old flute carved out of vulture bone in the newspaper a little while ago—wind instruments are a little more mysterious than strings, partly because their mechanism is invisible.
当然，乐器种类繁多。有些乐器，比如长笛和竖笛，两端都是开口的；而单簧管、双簧管和长号则是一端封闭的（尽管它们也有供人吹气的开口）。但所有这些乐器都是通过注入空气（通常是通过口腔）来产生振动，从而发出声音的。
There are different kinds of winds, of course. Some, like flutes and recorders, are open at both ends, while clarinets and oboes and trombones are closed at one end (even though they have openings for someone to blow in). But all of them make music when an infusion of air, usually from your mouth, causes a vibration of the air column inside the instrument.
当你向管乐器内吹气或施加压力时，就像拨动吉他弦或用弓拉动小提琴弦一样——通过向空气柱传递能量，你释放出了一系列频率范围的能量。空气进入空腔后，空气柱会根据自身长度选择共振频率。虽然难以想象，但计算起来却相对容易：乐器内部的空气柱会找到自身的基频以及一些高次谐波，并开始以这些频率振动。一旦空气柱开始振动，它就会像振动的音叉叉臂一样，推动和拉动空气，将声波传递到听众的耳朵。
When you blow or force air inside a wind instrument it’s like plucking a guitar string or exciting a violin string with a bow—by imparting energy to the air column, you are dumping a whole spectrum of frequencies into that air cavity, and the air column itself chooses the frequency at which it wants to resonate, depending mostly on its length. In a way that is hard to imagine, but with a result that’s relatively easy to calculate, the air column inside the instrument will pick out its fundamental frequency, and some of the higher harmonics as well, and start vibrating at those frequencies. Once the air column starts vibrating, it pushes and pulls on the air, just like vibrating tuning fork prongs, sending sound waves toward the ears of the listeners.
双簧管、单簧管和萨克斯管，都是通过吹奏簧片，将能量传递给空气柱，使其产生共鸣。长笛、短笛和竖笛，则是通过演奏者对着音孔或吹嘴吹气来产生共鸣。而铜管乐器，则需要你紧闭双唇，向乐器中吹出一种嗡嗡声——如果你没有接受过训练，几乎是不可能做到的。我最后只能往那玩意儿里吐口水！
With oboes, clarinets, and saxophones, you blow on a reed, which transfers energy to the air column and makes it resonate. For flutes and piccolos and recorders, it’s the way the player blows across a hole or into a mouthpiece that creates the resonance. And for brass instruments, you have to put your lips together tightly and blow a kind of buzz into the instrument—if you haven’t been trained to do it, it’s all but impossible. I end up just spitting into the damn thing!
如果乐器两端开口，例如长笛或短笛，空气柱就会像弦乐器一样，以其所有谐波振动，每个谐波都是基频的倍数。对于一端封闭、另一端开口的木管乐器，管子的形状至关重要。如果管径是圆锥形的，例如双簧管或萨克斯管，这些乐器会像长笛一样产生所有谐波。然而，如果管径是圆柱形的，例如单簧管，空气柱只会以基频的奇数倍振动：三倍、五倍、七倍等等。由于一些复杂的原因，所有铜管乐器都会像长笛一样产生所有谐波。
If the instrument is open at both ends, like a flute or piccolo, the air column can vibrate at its harmonics, each of which is a multiple of the fundamental frequency, as was the case with the strings. For woodwind instruments that are closed at one end and open at the other, the shape of the tube matters. If the bore is conical, such as the oboe or saxophone, the instruments will produce all harmonics like the flute. However, if the bore is cylindrical, such as the clarinet, the air column will only resonate at the odd-number multiples of the fundamental: three times, five times, seven times, and so on. For complicated reasons, all brass instruments resonate at all harmonics, like the flute.
更直观的解释是，空气柱越长，产生的声音频率和音调就越低。如果管子的长度减半，基频的频率就会加倍。这就是为什么短笛能吹奏出如此高的音符，而巴松管能吹奏出如此低的音符。这个普遍原理也解释了为什么管风琴的管子长度范围如此之广——有些管风琴可以发出跨越九个八度的声音。要产生一个基频，需要一根巨大的管子——64英尺长（19.5米，两端开口）。大约8.7赫兹，远低于人耳可听见的频率，但你能感觉到振动。这种巨大的管子全世界只有两根，因为它们实在没什么实用价值。长度只有现在十分之一的管子会产生频率高十倍的基频，即87赫兹。长度只有现在百分之一的管子则会产生大约870赫兹的基频。
What’s more intuitive is that the longer the air column is, the lower the frequency and the lower the pitch of the sound produced. If the length of a tube is halved, the frequency of the first harmonic will double. That’s why the piccolo plays such high notes, a bassoon plays such low ones. This general principle also explains why a pipe organ has such a range of pipe lengths—some organs can produce sounds across nine octaves. It takes an enormous tube—64 feet long (19.5 meters long, open on both sides) to produce a fundamental of about 8.7 hertz, literally below what the human ear can hear, though you can feel the vibrations. There are just two of these enormous pipes in the world, since they aren’t very practical at all. A tube ten times shorter will produce a fundamental ten times higher, thus 87 hertz. A tube a hundred times shorter will produce a fundamental of about 870 hertz.
管乐演奏者并非只是对着乐器吹气。他们还会通过按压或打开乐器上的小孔来有效地缩短或延长空气柱，从而升高或降低乐器发出的频率。这就是为什么当你玩儿童哨子时，用手指按住所有小孔，延长空气柱，就能发出低音。同样的原理也适用于铜管乐器。空气柱越长，即使需要绕圈，音调也会越低，也就是说，所有和声的频率都会降低。音调最低的大号，即降B调或BB调大号，其管长18英尺，基频约为30赫兹；额外的旋转阀可以将音调降低到20赫兹；而降B调小号的管长只有4.5英尺。小号或大号上的按钮可以打开或关闭额外的管子，从而改变共振频率的音调。长号是最容易用视觉方式理解的乐器。拉出滑管会增加空气柱的长度，从而降低其共振频率。
Wind instrumentalists don’t just blow into their instruments. They also close or open holes in their instruments that serve to effectively shorten or lengthen the air column, thereby raising or lowering the frequency it produces. That’s why, when you play around with a child’s whistle, the lower tones come when you put your fingers over all the holes, lengthening the air column. The same principle holds for brass instruments. The longer the air column, even if it has to go around in circles, the lower the pitch, which is to say, the lower the frequencies of all the harmonies. The lowest-pitched tuba, known as the B-flat or BB-flat tuba, has an 18-foot-long tube with a fundamental of about 30 hertz; additional, so-called rotary valves can lower the tone to 20 hertz; the tube of a B-flat trumpet is just 4.5 feet long. The buttons on a trumpet or tuba open or close additional tubes, changing the pitch of the resonant frequencies. The trombone is the simplest to grasp visually. Pulling the slide out increases the length of the air column, lowering its resonant frequencies.
我在课堂上用木制滑管长号演奏《铃儿响叮当》，学生们都很喜欢——我从没告诉过他们这是我唯一会吹的曲子。事实上，我的音乐天赋实在太差了，无论我讲过多少遍，每次演奏前都得练习。我甚至还在滑管上做了标记——其实是音符——标上了1、2、3等等；我根本不识谱。但正如我之前所说，我完全没有音乐天赋，但这并没有阻止我欣赏音乐之美，也没有阻止我享受音乐带来的乐趣。
I play “Jingle Bells” on a wooden slide trombone in my class, and the students love it—I never tell them it’s the only tune I can play. In fact, I’m so challenged as a musician that no matter how many times I’ve given the lecture, I still have to practice beforehand. I’ve even made marks on the slide—notes, really—numbered 1, 2, 3, and so forth; I can’t even read musical notes. But as I said before, my complete lack of musical talent hasn’t stopped me from appreciating music’s beauty, or from having lots of fun experimenting with it.
我写这篇文章的时候，正在饶有兴致地做个实验，研究一升装塑料苏打水瓶内的空气柱。这根本不是一个完美的空气柱，因为瓶颈部分逐渐扩大到瓶身直径。瓶子。瓶颈的物理原理可能非常复杂，正如你所想。但管乐器音乐的基本原理——空气柱越长，共振频率越低——仍然适用。你可以轻松地尝试一下。
While I’m writing this, I’m having some fun experimenting with the air column inside a one-liter plastic seltzer bottle. It’s not at all a perfect column, since the bottleneck gradually widens to the full diameter of the bottle. The physics of a bottleneck can get really complicated, as you might imagine. But the basic principle of wind instrument music—the longer the air column, the lower the resonant frequencies—still holds. You can try this easily.
把一个空的汽水瓶或葡萄酒瓶装满水，几乎装满，然后试着对着瓶口吹气。这需要一些练习，但很快你就能让空气柱以其共振频率振动。一开始声音会比较尖锐，但你喝的水越多（你明白我为什么建议用水了吧），空气柱就会越长，基频的音调就会降低。我还发现，空气柱越长，声音就越悦耳。基频越低，就越容易产生更高频率的谐波，声音的音色也会更加丰富。
Fill up an empty soda or wine bottle nearly to the top (with water!) and try blowing across the top. It takes some practice, but pretty soon you will get the air column to vibrate at its resonance frequencies. The sound will be high pitched at first, but the more you drink (you see why I suggested water), the longer the column of air becomes, and the pitch of the fundamental goes down. I also find that the longer I make the air column, the more pleasing the sound is. The lower the frequency of the first harmonic, the more likely it is that I will generate additional harmonics at higher frequencies, and the sound will have a more complex timbre.
你可能觉得声音是瓶子像琴弦一样振动产生的，而且你确实能感觉到瓶子在振动，就像你能感觉到萨克斯管振动一样。但实际上，是瓶子内部的空气柱在共振。为了更好地理解这一点，请思考以下问题：如果你拿两个相同的酒杯，一个空的，一个半满，分别用勺子轻轻敲击或用湿手指摩擦杯口来激发它们的第一谐波，哪个频率更高？为什么？我知道我故意让你给出错误答案，所以问这个问题可能不太公平——抱歉！但或许你能自己找到答案。
You might be thinking that it’s the bottle vibrating, just as the string did, that makes the sound, and you do in fact feel the bottle vibrating, just the way you might feel a saxophone vibrate. But again, it’s the air column inside that resonates. To drive home this point, consider this puzzle. If you take two identical wineglasses, one empty and one half full, and excite the first harmonic of each by tapping each glass lightly with a spoon or by rubbing its rim with a wet finger, which frequency will be higher, and why? It’s not fair of me to ask this question as I have been setting you up to give the wrong answer—sorry! But perhaps you’ll work it out.
同样的原理也适用于那些30英寸长的彩色波纹塑料管，也就是所谓的旋转管或类似的东西，你可能见过或者玩过。你还记得它们是怎么工作的吗？当你开始在头顶旋转一根旋转管时，首先会听到一个低频音。当然，你会以为这是第一谐波，就像我第一次玩这个玩具时一样。然而，不知为何，我始终无法激发出第一谐波。我总是先听到第二谐波。随着旋转速度的加快，你可以激发出越来越高的谐波。网上广告声称这些旋转管可以发出四个音调，但你可能只能听到三个——第四个音调，也就是第五谐波，这需要非常非常快的旋转。我计算了30英寸长管的前五个谐波频率，分别是223赫兹（我从未测出过这个频率）、446赫兹、669赫兹、892赫兹和1115赫兹。音调很快就变得很高。
The same principle is at play with those 30-inch flexible corrugated colored plastic tubes, called whirling tubes or something similar, which you’ve probably seen or played with. Do you remember how they work? When you start by whirling one around your head, you first hear a low-frequency tone. Of course, you expect this to be the first harmonic, just like I did when I first played with this toy. However, somehow I have never succeeded in exciting the first harmonic. It’s always the second that I hear first. As you go faster, you can excite higher and higher harmonics. Advertisements online claim you can get four tones from these tubes, but you may only get three—the fourth tone, which is the fifth harmonic, takes some really, really fast whirling. I calculated the frequencies of the first five harmonics for a tube length of 30 inches and find 223 hertz (I’ve never gotten this one), 446 hertz, 669 hertz, 892 hertz, and 1,115 hertz. The pitch gets pretty high pretty quickly.
危险共鸣
Dangerous Resonance
共振的物理原理远不止课堂演示那么简单。想想不同的乐器能营造出怎样的音乐氛围。音乐的共振触动着我们的情感，带给我们欢快、焦虑、平静、敬畏、恐惧、喜悦、悲伤等等。难怪我们会谈到体验情感共鸣，它能创造一段充满丰富与深度的关系，其中蕴含着理解、温柔和渴望的微妙情感。我们渴望与他人“和谐共鸣”绝非偶然。而当我们失去这种共鸣时，无论是暂时的还是永久的，那种痛苦又该有多么强烈？曾经的和谐变成了不和谐的干扰和情感的噪音。想想爱德华·阿尔比的小说《谁害怕弗吉尼亚·伍尔夫？》中的乔治和玛莎这两个角色。他们争吵得非常激烈。一对一的争吵只会激起他们的怒火，对客人来说也只是一场表演。但当他们联手对付客人时，危险性就大大增加了。
The physics of resonance reaches far beyond classroom demonstrations. Think of the different moods that music can produce with these different instruments. Musical resonance speaks to our emotions, bringing us gaiety, anxiety, calm, awe, fear, joy, sorrow, and more. No wonder we talk of experiencing emotional resonance, which can create a relationship filled with richness and depth, and overtones of understanding and tenderness and desire. It’s hardly accidental that we want to be “in tune” with someone else. And how painful when we lose that resonance, either temporarily or forever, and what had felt like harmony turns into discordant interference and emotional noise. Think of the characters George and Martha in Edward Albee’s Who’s Afraid of Virginia Woolf? They fight atrociously. When the fight is one on one, they create heat, and they remain just a show for their guests. They’re much more dangerous when they join forces to play get the guest.
在物理学中，共振也可能造成巨大的破坏。近代史上最壮观的破坏性共振案例发生在1940年11月，当时一股侧风恰好吹向塔科马海峡大桥的主跨。这座工程奇迹（因其上下摆动而被戏称为“飞奔的格蒂”）开始发生强烈的共振。随着侧风加剧桥梁摆动的幅度，桥体开始振动和扭曲，随着扭曲程度越来越剧烈，桥跨最终断裂，坠入水中。您可以在www.youtube.com/watch?v=j-zczJXSxnw观看这段壮观的坍塌视频。
Resonance can become powerfully destructive in physics too. The most spectacular example of destructive resonance in recent history occurred in November 1940, when a crosswind hit the main span of the Tacoma Narrows Bridge just right. This engineering marvel (which had become known as Galloping Gertie for its oscillations up and down) started to resonate powerfully. As the crosswind increased the amplitude of the bridge oscillations, the structure began to vibrate and twist, and as the twisting grew more and more extreme, the span tore apart, crashing into the water. You can watch this spectacular collapse at www.youtube.com/watch?v=j-zczJXSxnw.
九十年前，在法国昂热，一座横跨缅因河的悬索桥在478名士兵列队过桥时坍塌。他们步伐整齐地行进。行进的节奏在桥面上产生了共振，导致一些腐蚀的缆绳断裂；200多名士兵坠入河中身亡。这场灾难使法国的悬索桥建造停滞了二十年。1831年，英国军队在布劳顿悬索桥上步伐整齐地行进时，桥面发生共振，拉出桥梁一端的螺栓，导致桥梁坍塌。虽然无人伤亡，但英国军队从此命令所有过桥的部队都要打破行进的步伐。
Ninety years earlier, in Angers, France, a suspension bridge over the Maine River collapsed when 478 soldiers crossed it in military formation, marching in step. Their marching excited a resonance in the bridge, which snapped some corroded cables; more than 200 soldiers died when they fell into the river below. The disaster stopped suspension bridge building in France for twenty years. In 1831, British troops marching in step across the Broughton Suspension Bridge caused the bridge deck to resonate, pull out a bolt at one end of the bridge, and collapse. No one was killed, but the British army instructed all troops crossing bridges from then on to do so by breaking their marching step.
伦敦千禧桥于2000年通车，成千上万的行人发现桥身摇晃不定（工程师称之为横向共振）；仅仅几天后，当局就不得不关闭这座桥长达两年之久，期间安装阻尼器以控制行人脚步产生的晃动，场面一度十分尴尬。就连纽约市的布鲁克林大桥也曾让行人感到害怕。2003年，一场大停电期间，桥上挤满了行人，他们感受到桥面的横向摇晃，导致一些人感到不适。
The Millennium Bridge in London opened in 2000, and many thousands of pedestrians discovered that it wobbled a good bit (it had what engineers call lateral resonance); after just a few days authorities closed the bridge for two embarrassing years while they installed dampers to control the movement generated by pedestrian footsteps. Even the great Brooklyn Bridge in New York City frightened pedestrians who packed the bridge during a 2003 electrical blackout and felt a lateral swaying in the deck that made some of them sick.
在这种情况下，行人对桥梁的重量比通常通行的车辆更大，即使他们步伐不一致，双脚的共同运动也会在桥面上引发共振——也就是晃动。当桥梁向一个方向晃动时，行人会通过向相反方向迈步来抵消晃动，从而放大晃动的幅度。即使是工程师也承认，他们对人群对桥梁的影响了解甚少。幸运的是，他们非常了解如何建造能够抵御强风和地震的摩天大楼，这些强风和地震可能会产生共振频率，从而摧毁这些建筑。试想一下——我们祖先35000年前吹奏的笛子发出哀婉声音的原理，同样也可能威胁到雄伟壮丽的布鲁克林大桥和世界上最高的建筑。
In such situations pedestrians put more weight on a bridge than the cars that are usually crossing them, and the combined motion of their feet, even if they are not in step, can start to excite a resonance vibration—a wobble—on the bridge deck. When the bridge goes one way, they compensate by stepping the other way, magnifying the amplitude of the wobble. Even engineers admit they don’t know enough about the effects crowds can have on bridges. Fortunately, they know a lot about building skyscrapers that can resist the high winds and earthquakes that threaten to generate resonance frequencies that could destroy their creations. Imagine—the same principles that produced the plaintive sound of our ancestors’ 35,000-year-old flute could threaten the mighty and massive Brooklyn Bridge and the tallest buildings in the world.
第七章
CHAPTER 7
电力的奇妙之处
The Wonders of Electricity
这个方法在冬季效果最佳，因为那时空气非常干燥。确保你穿着涤纶衬衫或毛衣，然后在黑暗中站在镜子前，开始脱衣服。你可能会听到噼啪声，就像从烘干机里拿出衣服时一样（除非你用了那种不太浪漫的、用来减少耗电量的烘干纸）。但现在你还会看到几十个细小的火花闪闪发光。我喜欢做这个实验，因为它让我意识到物理学与我们的日常生活是多么贴近，只要我们知道如何去观察。而且，正如我喜欢跟我的学生指出的那样，事实上，如果你和朋友一起做这个小实验，会更有趣。
This works best in the winter, when the air is very dry. Make sure you’re wearing a polyester shirt or sweater, then stand in front of a mirror when it’s dark and start taking your shirt or sweater off. You will have anticipated that you’ll hear crackling noises, just like when you pull laundry out of the dryer (unless you use one of those unromantic dryer sheets designed to reduce all that electricity). But now you will also see the glow of dozens of teeny-weeny little sparks. I love doing this because it reminds me just how close physics is to our everyday experience, if only we know how to look for it. And, as I like to point out to my students, the truth is, this little demonstration is even more fun if you do it with a friend.
你知道，冬天走过地毯，伸手去拉门把手时——是不是感觉有点刺痛？——你可能会被电到，你知道那是静电造成的。你可能也曾因为和朋友握手而电到过她，或者把大衣交给衣帽间寄存时被电到过。坦白说，感觉冬天静电无处不在。梳头的时候，你能感觉到头发被静电分散开来，有时……摘下帽子后，它就能自己立起来了。冬天究竟有什么魔力，为什么总是火花四溅？
You know that whenever you walk across a rug in winter and reach for a doorknob—are you wincing?—you may get a shock, and you know that it’s from static electricity. You’ve probably even shocked a friend by shaking her hand, or felt a shock when you’ve handed your overcoat to a coat checker. Frankly, it feels like static electricity is everywhere in wintertime. You can feel your hair separating when you brush it, and sometimes it stands up on its own after you take your hat off. What is it about winter, and why are so many sparks flying?
所有这些问题的答案都要从古希腊人说起，他们是第一个命名并记录下我们今天所知的电现象的民族。早在两千多年前，希腊人就发现，如果用琥珀——他们和埃及人用来制作珠宝的化石树脂——摩擦布料，琥珀就能吸引干树叶。摩擦足够多次后，甚至还能产生电击。
The answer to all these questions begins with the ancient Greeks, who were the first to name and make a written record of the phenomenon we’ve come to know as electricity. Well over two thousand years ago, the Greeks knew that if you rubbed amber—the fossilized resin that they and the Egyptians made into jewelry—on a cloth, the amber could attract pieces of dry leaves. After enough rubbing, it could even produce a jolt.
我读过一些故事，说古希腊人在聚会上无聊时，女人们会把琥珀首饰蹭到衣服上，然后让首饰碰到青蛙。青蛙当然会跳起来，拼命想逃离这些疯狂的聚会者，这显然给古人带来了很多乐趣。这些故事完全不合逻辑。首先，你能想象有多少聚会上会有那么多青蛙等着被醉醺醺的狂欢者电击吗？其次，稍后我会解释原因，静电在青蛙比较活跃的月份，以及空气潮湿的时候——尤其是在希腊——并不那么有效。不管这个故事的真假，不可否认的是，希腊语中“琥珀”一词是“电子”（electron），所以实际上是希腊人给电命名的，就像他们给宇宙中许多其他事物命名一样，无论大小。
I’ve read stories claiming that when Greeks were bored at parties, the women would rub their amber jewelry on their clothing and touch the jewelry to frogs. The frogs would jump, of course, desperately trying to escape the crazy partiers, which apparently made for great fun among the ancients. Nothing about these stories makes any sense. First off, how many parties can you imagine where there are lots of frogs waiting around to be shocked by drunken revelers? Secondly, for reasons I’ll explain in a bit, static electricity doesn’t work so well during the months when you’re more likely to see frogs, and when the air is humid—especially in Greece. Whatever the truth of this story, what is undeniable is that the Greek word for “amber” is electron, so it was really the Greeks who named electricity, along with so much else of the universe, both large and small.
十六、十七世纪的欧洲物理学家们，在物理学还被称为自然哲学的年代，对原子及其组成成分一无所知，但他们却是杰出的观察者、实验家和发明家，其中一些人也是杰出的理论家。这些人包括第谷·布拉赫、伽利略·伽利莱、约翰内斯·开普勒、艾萨克·牛顿、勒内·笛卡尔、布莱兹·帕斯卡、罗伯特·胡克和罗伯特·波义耳、戈特弗里德·莱布尼茨、克里斯蒂安·惠更斯——他们都在不断发现新事物、撰写著作、彼此辩论，并彻底颠覆了中世纪的经院哲学。
The European physicists of the sixteenth and seventeenth centuries, when physics was known as natural philosophy, didn’t know anything about atoms or their components, but they were terrific observers, experimenters, and inventors, and some were fantastic theorists as well. You had Tycho Brahe, Galileo Galilei, Johannes Kepler, Isaac Newton, René Descartes, Blaise Pascal, Robert Hooke and Robert Boyle, Gottfried Leibniz, Christiaan Huygens—all making discoveries, writing books, disputing one another, and turning medieval scholasticism upside down.
到了18世纪30年代，英国、法国和美国等地已经开展了真正意义上的电学科学研究（而非哗众取宠的把戏）。当然，费城的实验者们都发现，如果用丝绸摩擦玻璃棒，玻璃棒就会带上某种电荷（我们称之为A），但如果用同样的方法摩擦琥珀或橡胶，它们就会带上另一种电荷（我们暂且称之为B）。他们之所以知道这两种电荷不同，是因为当他们把两根都用丝绸摩擦过的、带电荷A的玻璃棒放在一起时，它们会相互排斥，这种排斥力完全看不见，但却可以感知。同样，带电荷B的物体也会相互排斥。然而，带不同电荷的物体，比如一根带电荷A的玻璃棒和一根带电荷B的橡胶棒，却会相互吸引而不是排斥。
By the 1730s, genuine scientific study of electricity (as opposed to putting on parlor tricks) was well under way in England, France, and, of course, Philadelphia. All of these experimenters had figured out that if they rubbed a glass rod with a piece of silk it would gain a charge of some kind (let’s call it A)—but if they rubbed amber or rubber in the same way it would acquire a different charge (let’s call it B for now). They knew that the charges were different because when they took two glass rods that they’d rubbed with silk, both charged with A, and put them near each other, they would repel each other, by some completely invisible but nevertheless palpable force. Similar objects that had been charged with charge B also repelled each other. And yet differently charged objects, say a charged glass rod (A) and a charged rubber rod (B), would attract rather than repel each other.
摩擦使物体带电是一种非常奇妙的现象，它甚至还有一个很美的名字——“摩擦起电效应”，源自希腊语中“摩擦”一词。人们可能会觉得是两个物体之间的摩擦产生了电荷，但事实并非如此。实际上，有些材料会贪婪地吸引电荷B，而另一些材料则会迫不及待地释放电荷A。摩擦之所以有效，是因为它增加了物质之间的接触点，从而促进了电荷的转移。许多材料构成了一个“摩擦电序列”（你可以在网上轻松找到），序列上两个材料的位置越远，它们就越容易相互带电。
Charging objects by rubbing them is a truly intriguing phenomenon, and it even has a wonderful name, the “triboelectric” effect, from the Greek word for “rubbing.” It feels as though the friction between the two objects is what produces the charge, but that’s not the case. It turns out that some materials greedily attract charge B, while other materials can’t wait to lose it, thereby creating charge A. Rubbing works because it increases the number of contact points between substances, facilitating the transfer of charge. There is a ranked list of many materials that make up the “triboelectric series” (you can find it easily online), and the farther apart two materials are on the scale, the more easily they can charge each other.
以梳子通常由塑料或硬橡胶制成为例。它们在摩擦电序列中与人类头发的电荷相差甚远，这就解释了为什么冬天梳头时头发很容易产生火花并竖起来——尤其是我的头发。想想看：不仅会产生火花，因为用力梳头会使梳子和头发都带电；而且由于所有头发都带上了相同的电荷（无论是什么电荷），每根带电的头发都会排斥其他带相同电荷的头发，这时我就像个疯狂的科学家。当你用鞋子在地毯上摩擦时，你会带上A或B电荷，具体取决于鞋底和地毯的材质。当你被附近的门把手电到时，你的手要么是从门把手上带电，要么是从地毯上带电。向它发射电击。你发射的是哪种电击都无所谓；反正你都会感到电击！
Take plastic or hard rubber that combs are typically made of. They are pretty far away from human hair in the triboelectric series, which accounts for how easily your hair can spark and stand up when you comb it in winter—especially my hair. And think about it: not only does it spark, since by vigorously combing my hair I am charging both the comb and my hair; but since the hair all picks up the same charge, whichever it is, each charged hair repels all the other like-charged hairs, and I start to resemble a mad scientist. When you scuff your shoes on a carpet, you charge yourself with A or B, depending on the material of your shoe soles and the carpet. When you get shocked by the nearest doorknob, your hand is either receiving charge from the doorknob or shooting charge to it. It doesn’t matter to you which charge you have; either way, you feel the shock!
正是本杰明·富兰克林——外交家、政治家、编辑、政治哲学家、双焦眼镜、游泳脚蹼、里程表和富兰克林炉的发明者——提出了所有物质都渗透着他称之为“电流体”或“电火”的观点。由于这一理论似乎能够解释其他自然哲学家的实验结果，因此它极具说服力。例如，英国人斯蒂芬·格雷已经证明，电流可以通过金属导线远距离传导，因此，通常不可见的流体或火（毕竟，火花确实很像火）的概念就显得合情合理了。
It was Benjamin Franklin—diplomat, statesman, editor, political philosopher, inventor of bifocals, swim fins, the odometer, and the Franklin stove—who introduced the idea that all substances are penetrated with what he called “electric fluid,” or “electric fire.” Because it seemed to explain the experimental results of his fellow natural philosophers, this theory proved very persuasive. The Englishman Stephen Gray, for instance, had shown that electricity could be conducted over distances in metal wire, so the idea of a usually invisible fluid or fire (after all, sparks do resemble fire) made good sense.
富兰克林认为，如果火势过盛，则带正电；如果火势不足，则带负电。他还引入了正负号的约定，并决定，如果用羊毛或丝绸摩擦玻璃（产生A电荷），就使玻璃带上了过量的火，因此应该称之为正电荷。
Franklin argued that if you get too much of the fire then you’re positively charged, and if you have a deficiency of it then you’re negatively charged. He also introduced the convention of using positive and negative signs and decided that if you rub glass with a piece of wool or silk (producing the A charge) you give it an excess of fire, and therefore it should be called positive.
富兰克林并不知道电的成因，但他提出的“电流体”理论既精妙又实用，即便并非完全正确。他认为，如果将这种流体从一种物质转移到另一种物质中，那么流体过剩的物质就会带正电，而流体流出的物质则会带负电。富兰克林发现了电荷守恒定律，该定律指出电荷既不能凭空产生，也不能凭空消失。如果你产生了一定量的正电荷，那么你也必然会产生等量的负电荷。电荷的流动是一个零和博弈——正如物理学家所说，电荷守恒。
Franklin didn’t know what caused electricity, but his idea of an electrical fluid was brilliant as well as useful, even if not exactly correct. He maintained that if you take the fluid and bring it from one substance to another, the one with an excess becomes positively charged and, at the same time, the one from which you take the fluid becomes negatively charged. Franklin had discovered the law of conservation of electric charge, which states that you cannot truly create or get rid of charge. If you create a certain amount of positive charge, then you automatically create the same amount of negative charge. Electric charge is a zero-sum game—as physicists would say, charge is conserved.
富兰克林和我们今天一样，都明白同种电荷（正电荷与正电荷、负电荷与负电荷）相互排斥，异种电荷（正电荷与负电荷）相互吸引。他的实验表明，物体带的电荷越多，彼此距离越近，它们之间的作用力（无论是吸引力还是排斥力）就越强。他还像格雷和同时期的其他科学家一样，发现某些物质有些物质能导电，有些物质能导火——我们现在称这些物质为导体——而有些物质不能导电，因此被称为非导体或绝缘体。
Franklin understood, as we do today, that like charges (positive and positive, negative and negative) repel each other, and that opposite charges (positive and negative) attract. His experiments showed him that the more fire objects had, and the closer they were to each other, the stronger the forces, whether of attraction or repulsion. He also figured out, like Gray and others around the same time, that some substances conduct the fluid or fire—we now call those substances conductors—and others do not, and are therefore called nonconductors, or insulators.
富兰克林没弄明白的是，火究竟是由什么构成的。如果它不是火或液体，那它是什么？而且，为什么冬天似乎火的种类更多——至少在我居住的美国东北部地区是这样，让我们时不时感到震惊？
What Franklin had not figured out is what the fire really consists of. If it’s not fire or fluid, what is it? And why does there seem to be so much more of it in the winter—at least where I live, in the northeastern United States, shocking us right and left?
在我们深入原子内部探究电火的本质之前，我们需要认识到，电在我们世界中的渗透远超富兰克林的认知，也远超我们大多数人的想象。它不仅维系着我们日常生活中大部分的体验，也使我们所见、所闻、所做之事成为可能。我们之所以能够思考、感受、沉思和惊叹，是因为电荷在我们大脑中约1000亿个细胞中数以百万计的细胞之间跳跃。同时，我们之所以能够呼吸，是因为神经产生的电脉冲驱动着胸部的不同肌肉进行复杂的运动，如同交响乐般交响。例如，最简单的例子就是，当横膈膜收缩并下降到胸腔时，它会扩张胸腔，将空气吸入肺部。当横膈膜放松并再次向上扩张时，它会将空气排出肺部。如果没有无数微小的电脉冲不断地在体内传递信息，所有这些运动都不可能实现。这些电脉冲负责告诉肌肉收缩，然后停止收缩，让其他肌肉接替它们的工作。来回往复，来回往复，直到生命的尽头。
Before we take a look inside the atom to grapple with the nature of electric fire, we need to see that electricity pervades our world far more than Franklin knew—and far more than most of us realize. It not only holds together most of what we experience on a daily basis; it also makes possible everything we see and know and do. We can only think and feel and muse and wonder because electric charges jump between uncountable millions of the roughly 100 billion cells in our brains. At the same time, we can only breathe because electric impulses generated by nerves cause different muscles of our chest to contract and relax in a complicated symphony of movements. For example, and most simply, as your diaphragm contracts and drops in your thorax, it enlarges the chest cavity, drawing air into the lungs. As it relaxes and expands upward again, it pushes air out of the lungs. None of these motions would be possible without countless tiny electric impulses constantly sending messages throughout your body, in this case telling muscles to contract and then to stop contracting while others take up the work. Back and forth, back and forth, for as long as you live.
我们的眼睛之所以能看见，是因为视网膜上的微小细胞——视杆细胞和视锥细胞——分别负责感知黑白和色彩，它们被探测到的物体刺激后，会通过视神经向大脑发送电信号。然后，大脑会判断我们看到的是水果摊还是摩天大楼。大多数汽车都以汽油为动力，尽管混合动力汽车越来越多地使用电力，但如果没有电力从电池经由点火系统输送到气缸，任何发动机都不会使用汽油。在气缸中，电火花会引发可控的爆炸，每分钟发生数千次。由于分子形成于……如果没有电，将原子结合在一起的电场力，化学反应（例如汽油燃烧）将不可能发生。
Our eyes see because the tiny cells of our retinas, the rods and cones that pick up black-white and colors, respectively, get stimulated by what they detect and shoot off electric signals through the optic nerves to our brains. Our brains then figure out whether we’re looking at a fruit stand or a skyscraper. Most of our cars run on gasoline, though hybrids use increasing amounts of electricity, but there would be no gasoline used in any engine without the electricity running from the battery through the ignition to the cylinders, where electric sparks ignite controlled explosions, thousands of them per minute. Since molecules form due to electric forces that bind atoms together, chemical reactions—such as gasoline burning—would be impossible without electricity.
因为有了电，马才能奔跑，狗才能喘气，猫才能伸展四肢。因为有了电，保鲜膜才能揉皱，包装胶带才能相互吸引，巧克力盒上的玻璃纸包装似乎永远也撕不下来。这份清单远非详尽无遗，但我们真的很难想象没有电的世界会是什么样子；没有电，我们甚至无法思考。
Because of electricity, horses run, dogs pant, and cats stretch. Because of electricity, Saran Wrap crumples, packing tape attracts itself, and the cellophane wrapping never seems to want to come off of a box of chocolates. This list is hardly exhaustive, but there’s really nothing that we can imagine existing without electricity; we could not even think without electricity.
当我们把目光转向比我们体内的微观细胞还要小的事物时，这个道理依然适用。地球上的每一份物质都由原子构成，而要真正理解电，我们必须深入原子内部，简要地观察它的组成部分：我们不必了解所有部分，因为那样会变得极其复杂，但我们只需要了解我们需要的部分。
That holds true when we turn our focus to things even smaller than the microscopic cells in our bodies. Every bit of matter on Earth consists of atoms, and to really understand electricity we have to go inside the atom and briefly look at its parts: not all of them now, because that gets incredibly complicated, but just the parts we need.
原子本身非常微小，只有最强大、最精巧的仪器——扫描隧道显微镜、原子力显微镜和透射电子显微镜——才能观测到它们。（网上有一些用这些仪器拍摄的令人惊叹的图像。您可以通过以下链接查看部分图像：www.almaden.ibm.com/vis/stm/gallery.html。）
Atoms themselves are so tiny that only the most powerful and ingenious instruments—scanning tunneling microscopes, atomic force microscopes, and transmission electron microscopes—can see them. (There are some astonishing images from these instruments on the web. You can see some at this link: www.almaden.ibm.com/vis/stm/gallery.html.)
如果我取65亿个原子（大致相当于地球上的人口数量），将它们排成一排，彼此紧挨着，那排大约有两英尺长。但比每个原子还要小，大约小一万倍的，是原子核。原子核包含带正电的质子和中子。中子，顾名思义，是电中性的，它们不带任何电荷。质子（希腊语意为“第一个”）的质量与中子大致相同——大约只有千克的二十亿分之一（2 × 10⁻²⁷ ）。因此，无论原子核有多少个质子和中子——有些原子核甚至超过两百个——它仍然非常轻。而且非常小：直径只有大约一万亿分之一厘米。
If I were to take 6.5 billion atoms, roughly the same as the number of people on Earth, and line them up in a row, touching one another, I would have a line about 2 feet long. But even smaller than every atom, about ten thousand times smaller, is its nucleus, which contains positively charged protons and neutrons. The latter, as you might imagine from their name, are electrically neutral; they have no charge at all. Protons (Greek for “first one”) have about the same mass as the neutrons—the inconceivably small two-billionths of a billionth of a billionth (2 × 10–27) of a kilogram, approximately. So no matter how many protons and neutrons a nucleus has—and some have more than two hundred—it remains a real lightweight. And tiny: just about a trillionth of a centimeter in diameter.
然而，要理解电学，最重要的是要明白质子带正电荷。虽然它本身并没有什么理由被称为正电荷，但自富兰克林以来，物理学家们一直把用丝绸摩擦玻璃棒后残留在玻璃棒上的电荷称为正电荷，因此质子也带正电荷。
Most important for understanding electricity, however, is that the proton has a positive charge. There’s no intrinsic reason for it to be called positive, but since Franklin, physicists have called the charge left on a glass rod after it’s been rubbed with silk positive, so protons are positive.
更重要的是，原子其余部分是由电子构成的——这些带负电荷的粒子围绕着原子核形成电子云，以亚原子尺度来看，它们与原子核的距离相当远。如果你手里拿着一个棒球，代表原子核，那么围绕着它的电子云可以延伸到半英里之外。显然，原子的大部分都是空的空间。
Even more important, it turns out, is the remainder of the atom, consisting of electrons—negatively charged particles that swarm around the nucleus in a cloud, at some distance by subatomic standards. If you hold a baseball in your hand, representing an atomic nucleus, the cloud of electrons around it would range as far as half a mile away. Clearly, most of the atom is empty space.
电子的负电荷强度与质子的正电荷强度相等。因此，质子数和电子数相同的原子和分子呈电中性。当它们不呈电中性，即电子过剩或不足时，我们称之为离子。正如我们在第六章讨论过的，等离子体是部分或完全电离的气体。地球上我们接触的大多数原子和分子都是电中性的。在室温下的纯水中，只有千万分之一的分子是电离的。
The negative charge of an electron is equal in strength to the positive charge of the proton. As a result, atoms and molecules that have the same number of protons and electrons are electrically neutral. When they are not neutral, when they have either an excess or deficit of electrons, we call them ions. Plasmas, as we discussed in chapter 6, are gases partially or fully ionized. Most of the atoms and molecules we deal with on Earth are electrically neutral. In pure water at room temperature only 1 in 10 million molecules are ionized.
根据富兰克林的约定，当某些物体拥有过多的电子时，我们称它们带负电；当它们缺少电子时，我们称它们带正电。用丝绸摩擦玻璃时，你会“擦掉”（某种程度上）很多电子，所以玻璃最终带正电。用同一块丝绸摩擦琥珀或硬橡胶时，它们会收集电子并带负电。
As a consequence of Franklin’s convention, when some objects have an overabundance of electrons, we say that they are negatively charged, and when they have a deficit of electrons, we say they have a positive charge. When you rub glass with a piece of silk you “rub off” (sort of) lots of electrons, so the glass ends up with a positive charge. When you rub amber or hard rubber with the same piece of silk, they collect electrons and develop a negative charge.
在大多数金属中，大量的电子完全脱离了原子核，或多或少地在原子间自由游走。这些电子特别容易受到外部电荷（正电荷或负电荷）的影响，当施加电荷时，它们会向电荷移动或远离电荷——从而产生电流。关于电流我还有很多要说的，但现在我只想指出，我们称这些材料为导体，因为它们很容易传导（允许）带电粒子，在这种情况下，带电粒子指的是电子。（离子也能产生电流，但不能在固体中产生电流，因此也不能在金属中产生电流。）
In most metals large numbers of electrons have escaped their atoms altogether and are more or less freely wandering around between atoms. These electrons are particularly susceptible to an external charge, either positive or negative, and when such a charge is applied, they move toward or away from it—thus creating electric current. I have a lot more to say about current, but for the time being I’ll just point out that we call these materials conductors, because they easily conduct (allow the movement of) charged particles, which in this case means electrons. (Ions can also create electric currents but not in solids, and thus not in metals.)
我喜欢电子随时准备活动、随时准备移动、随时准备响应正负电荷的想法。在非导体中，这种活动非常少见；所有电子都被牢牢地固定在它们的轨道上。单个原子。但这并不意味着我们不能用非导体——尤其是常见的橡胶非导电气球——来做一些有趣的事情。
I love the idea of electrons just ready to play, ready to move, ready to respond to positive or negative charges. In nonconductors, there’s very little action of this sort; all the electrons are well fixed to their individual atoms. But that doesn’t mean we can’t have some fun with nonconductors—especially your garden-variety, rubber, nonconducting balloon.
你可以准备一小包未充气的橡胶气球（细一点的气球效果更好，比如可以扭成动物形状的那种），来演示我刚才说的所有内容。因为大多数人手边都没有玻璃棒，我原本希望可以用玻璃杯、酒瓶甚至灯泡来代替，但尽管我尽力尝试，它们都不行。那么为什么不试试大的塑料梳子或硬橡胶梳子呢？准备一块丝绸、一条旧领带或围巾，或者你另一半一直想让你扔掉的夏威夷衬衫也会很有帮助。但如果你不介意弄乱头发——为了科学，谁会在意呢？——你也可以用自己的头发。你还需要把一些纸撕成几十片。数量多少并不重要，但它们应该很小，大约一角或一分硬币那么大。
You can demonstrate everything I’m talking about here by supplying yourself with a little pack of uninflated rubber balloons (thinner ones work better, like the ones you can twist into animals). Since most of you don’t have glass rods sitting around, I had hoped that a water glass or wine bottle or even a lightbulb might substitute, but despite my best efforts, they don’t. So why not try a large plastic or hard rubber comb? It will also be helpful to have a piece of silk, maybe an old tie or scarf, or a Hawaiian shirt your significant other has been trying to get you to throw out. But if you don’t mind getting your hair mussed—for the cause of science, who would mind?—you can make use of your own hair. And you’ll need to tear up some paper into, say, a few dozen or so pieces. The number doesn’t matter, but they should be small, about the size of a dime or penny.
和所有静电实验一样，这些实验在冬季（或午后沙漠的空气）效果更好，因为此时空气干燥而非潮湿。为什么呢？因为空气本身不是导体——事实上，它是一种很好的绝缘体。然而，如果空气中含有水分，电荷会因为一些复杂的原因而流失，我们这里就不赘述了。潮湿的空气不会让电荷在杆子、布料、气球或头发上积聚，而是会逐渐流失。这就是为什么只有在空气非常干燥的时候，你才会被门把手电到的原因。
Like all static electricity experiments, these work a lot better in winter (or in afternoon desert air), when the air is dry rather than moist. Why? Because air itself is not a conductor—in fact, it’s a pretty good insulator. However, if there is water in the air, charge can bleed away for complicated reasons which we will not discuss. Instead of allowing charge to build up on a rod or cloth or balloon, or your hair, humid air gradually bleeds charge away. That’s why you only have a problem getting shocked on doorknobs when the air is really dry.
隐形感应
Invisible Induction
准备好所有材料，开始体验电的奇妙之处吧！首先，用梳子在头发上用力摩擦，确保头发非常干燥，或者用丝绸摩擦梳子，给梳子充电。根据摩擦起电规律，我们知道梳子会带负电荷。现在，停下来想一想接下来会发生什么……当你把梳子靠近那堆纸屑时会发生什么？为什么？如果你说“什么都没发生”，我当然可以理解。
Assemble all your materials, and get ready to experience some of the wonders of electricity. First charge up your comb by rubbing it hard on your hair, making sure your hair is very dry, or rubbing it with the piece of silk. We know from the triboelectric series that the comb will pick up negative charge. Now, stop for a moment and think about what’s going to happen as you bring the comb close to the pile of paper bits, and why. I could certainly understand if you say “nothing at all.”
然后把梳子放在你那堆纸片上方几英寸的地方。慢慢放下梳子，看看会发生什么。是不是很神奇？再试一次——这可不是偶然。有些纸片会跳到梳子上，有些会粘在梳子上一会儿然后掉下来，还有一些则纹丝不动。事实上，如果你稍微摆弄一下梳子和纸片，你甚至可以让纸片竖起来，或者在梳子表面“跳舞”。这到底是怎么回事？为什么有些纸片会粘在梳子上，而另一些纸片会跳起来、接触一下然后又掉下来呢？
Then put the comb a few inches above your little mound of paper pieces. Slowly lower the comb and watch what happens. Amazing, isn’t it? Try it again—it’s no accident. Some of the bits of paper jump up to your comb, some stick to it for a bit and fall back down, and some stay fast. In fact, if you play around with the comb and the paper a bit, you can make the pieces of paper stand on edge, and even dance on the surface. What on earth is going on? Why do some pieces of paper stick to the comb, while others jump up, touch, and fall right back down?
这些问题问得非常好，答案也十分精彩。事情是这样的：梳子上的负电荷会排斥纸张原子中的电子，因此，即使电子并非自由电子，它们也会在原子核的远端停留更长时间。当电子发生这种情况时，靠近梳子的原子核一侧的电荷会比之前略微增加一些。所以，纸张带正电的一侧会被梳子上的负电荷吸引，轻盈的纸张便会向上弹向梳子。为什么纸张的吸引力会超过梳子负电荷与纸张中电子之间的排斥力呢？这是因为电斥力（以及电吸引力）的大小与电荷的强度成正比，与它们之间距离的平方成反比。我们称之为库仑定律，它以做出这一重要发现的法国物理学家查尔斯·奥古斯丁·库仑的名字命名。你会注意到它与牛顿万有引力定律有着惊人的相似之处。请注意，我们还称电荷的基本单位为库仑，正电荷单位为 +1 库仑（约 6 × 10 18 个质子），而负电荷单位为 -1 库仑（约 6 × 10 18个电子）。
These are excellent questions, with very cool answers. Here’s what happens. The negative charge on the comb repels the electrons in the paper atoms so that, even though they’re not free, they spend just a little more time on the far side of their atoms. When they do so, the sides of the atoms nearest the comb are just a tiny bit more positively charged than they had been before. So, the positive-leaning edge or side of the paper is attracted to the negative charge on the comb, and the very lightweight paper jumps up toward the comb. Why does their attractive force win out over the repulsive force between the comb’s negative charge and the electrons in the paper? It’s because the strength of electrical repulsion—and attraction—is proportional to the strength of the charges, but inversely proportional to the square of the distance between them. We call this Coulomb’s law, named after the French physicist Charles-Augustin de Coulomb, who made this important discovery, and you will notice its astonishing similarity to Newton’s law of universal gravitation. Note that we also call the basic unit of charge the coulomb, and the positive unit of charge is +1 coulomb (about 6 × 1018 protons), while the negative charge is –1 coulomb (about 6 × 1018 electrons).
库仑定律告诉我们，即使正负电荷之间的距离只有很小的差别，也会产生很大的影响。换句话说，距离较近的电荷之间的吸引力会超过距离较远的电荷之间的排斥力。
Coulomb’s law tells us that even a very small difference in the distance between the positive charges and the negative charges can have a large effect. Or put differently, the attractive force of the nearer charges overpowers the repelling force of the more distant charges.
我们将整个过程称为感应，因为当我们把带电物体靠近中性物体时，实际上是在中性物体的近侧和远侧感应出电荷，从而在纸片上产生一种电荷极化。你可以在我在MIT World上为孩子和家长制作的名为“电磁的奇妙之处”的讲座中看到这个小演示的几个版本，你可以在这里找到： http: //mitworld.mit.edu/video/319。
We call this entire process induction, since what we are doing when we bring a charged object toward a neutral one is inducing charge on the near and far sides of the neutral object, creating a kind of charge polarization in the pieces of paper. You can see several versions of this little demonstration in my lecture for kids and their parents called “The Wonders of Electricity and Magnetism” on MIT World, which you can find here: http://mitworld.mit.edu/video/319.
至于为什么有些纸片会立即落下而有些则会粘在梳子上，这也很有趣。当一张纸片接触到梳子时，梳子上的一些多余电子会转移到纸片上。这时，梳子和纸片之间可能仍然存在吸引力，但这种吸引力可能不足以抵消重力，因此纸片会落下。如果电荷转移量很大，电场力甚至可能变成斥力，在这种情况下，重力和电场力共同作用，会使纸片向下加速。
As for why some bits of paper fall right back down while some stay stuck, this is also interesting. When a piece of paper touches the comb, some of the excess electrons on the comb move to the paper. When that happens, there still may be an attractive electric force between the comb and the piece of paper, but it may not be large enough anymore to counter the force of gravity, and thus the piece of paper will fall down. If the charge transfer is high, the electric force may even become repelling, in which case both the force of gravity and the electric force will accelerate the piece of paper downward.
现在吹一个气球，把气球口打个结固定住，再系上一根绳子。找个家里可以自由悬挂气球的地方，比如吊灯上。或者你也可以在绳子上挂个重物，让气球从厨房桌子上垂下来，大约六英寸到一英尺。用丝绸或头发用力摩擦梳子，再次给它充电——记住，摩擦越多，充电越强。慢慢地把梳子靠近气球。你觉得会发生什么？
Now blow up a balloon, knot the end so it stays blown up, and tie a string to the end. Find a place in your house where you can hang the balloon freely. From a hanging lamp, perhaps. Or you can put a weight of some kind on the string and let the balloon hang down from your kitchen table, about six inches to a foot. Charge the comb again by rubbing it vigorously with the silk or on your hair—remember, more rubbing produces a stronger charge. Very slowly, bring your comb close to the balloon. What do you think is going to happen?
现在试试看。是不是也很奇怪？气球会向梳子移动。就像之前用纸一样，你的梳子在气球上产生了某种电荷分离（感应！）。那么，当你把梳子移得更远时会发生什么？为什么呢？你凭直觉就知道，气球会回到垂直位置。但现在你知道为什么了吧？当外部影响消失时，电子就没有理由再停留在各自原子的远端了。看看我们仅仅从这短短的实验中就推导出了什么！用梳子梳理头发，玩弄小纸片和药店买来的气球！
Now try it. Also pretty weird, right? The balloon moves toward the comb. Just like with the paper, your comb produced some kind of separation of charge on the balloon (induction!). So what will happen when you move the comb farther away—and why? You know, intuitively, that the balloon will return to its vertical position. But now you know why, right? When the external influence disappears, the electrons no longer have any reason to hang out a little more on the far side of their respective atoms. Look what we were able to deduce just from this little bit of rubbing a comb and playing with little pieces of paper and a drugstore balloon!
现在再吹几个气球。当你用力摩擦头发时会发生什么？没错，你的头发会开始出现奇怪的现象。为什么呢？因为在摩擦电序列中，人的头发位于正极，而橡胶气球则位于负极。换句话说，橡胶会从你的头发上吸收大量的电子，使你的头发带正电。由于同种电荷相互排斥，当每根发丝都带正电，并且想要远离其他带相同电荷的头发时，你的头发会做什么呢？你的发丝会相互排斥，使它们竖起来。当然，这和你冬天摘下针织帽时的情况也一样。帽子摩擦头发时会带走大量的电子，使你的发丝带正电，并渴望竖起来。
Now blow up some more of the balloons. What happens when you rub one vigorously on your hair? That’s right. Your hair starts to do weird things. Why? Because in the triboelectric series human hair is way at the positive end, and a rubber balloon is on the seriously negative side. In other words, rubber picks up a lot of the electrons from your hair, leaving your hair charged positively. Since like charges repel, what else can your hair do when each strand has a positive charge and wants to get away from all the other like-charged hairs? Your strands of hair are repelling one another, making them stand up. This is of course also what happens when you pull a knit hat off of your head in winter. In rubbing your hair, the hat takes lots of electrons away, leaving the strands of your hair positively charged and aching to stand up.
回到气球的话题。你已经用力地在头发上摩擦过气球了（摩擦涤纶衬衫的效果可能更好）。我想你应该知道我要说什么了吧？把气球贴在墙上，或者贴在你朋友的衬衫上。它会粘住。为什么呢？关键就在这里。当你摩擦气球时，它会带电。当你把气球贴在墙上时，墙的导电性很差，墙内原子周围的电子会感受到气球负电荷的斥力，它们会在远离气球的原子一侧停留更长时间，而在靠近气球的原子一侧停留更短时间——这就是感应！
Back to the balloons. So you’ve rubbed one vigorously on your hair (rubbing it on your polyester shirt may work even better). I think you know what I’m going to suggest, right? Put the balloon against the wall, or on your friend’s shirt. It sticks. Why? Here’s the key. When you rub the balloon, you charge it. When you hold the balloon against the wall, which is not much of a conductor, the electrons orbiting the atoms in the wall feel the repulsive force of the balloon’s negative charge and spend just a wee bit more time on the side of the atom farthest away from the balloon and a little bit less on the side closest to the balloon—that’s induction!
换句话说，气球接触墙面的地方会带上微弱的正电荷，带负电荷的气球会被吸引。这是一个非常神奇的结果。但是，为什么正负电荷不会相互抵消，电荷不会转移，导致气球立即掉落呢？这是一个很好的问题。首先，橡胶气球吸收了一些额外的电子。在橡胶这种非导体中，电子不易移动，所以电荷倾向于保持静止。不仅如此，你并没有让气球在墙上摩擦，产生大量的接触。它只是静静地待在那里，发挥着自身的吸引力。但它也靠摩擦力吸附在那里。还记得第三章里的旋转木马游乐设施吗？在这里，电力的作用就相当于旋转木马的向心力。气球可以吸附在墙上一段时间，直到电荷逐渐从气球上泄漏，通常会转移到空气中的水分上。（如果你的气球吸附不住，可能是空气太潮湿，导致空气导电性更好，或者你的气球太重——我建议用细气球就是出于这个原因。）
The surface of the wall, in other words, right where the balloon is touching it, will become slightly positively charged, and the negatively charged balloon will be attracted. This is a pretty amazing result. But why don’t the two charges—the positive and negative charges—just neutralize each other, with charges transferring, making the balloon immediately fall off? It’s a very good question. For one thing the rubber balloon has picked up some extra electrons. They don’t move around very easily in a nonconductor like rubber, so charges tend to stay put. Not only that, you’re not rubbing the balloon against the wall, making lots and lots of contact. It’s just sitting there, doing its attractive thing. But it’s also held there by friction. Remember the Rotor carnival ride back in chapter 3? Here the electric force plays the role played by the centripetal force of the Rotor. And the balloon can stay on the wall for some time, until the charge gradually leaks off the balloon, generally onto moisture in the air. (If your balloons don’t stick, the air is either too humid, making the air a better conductor, or your balloons might be too heavy—I suggested thin ones for just this reason.)
我喜欢在来听我公开讲座的孩子们身上粘气球。多年来，我一直在儿童生日派对上这样做，你也可以试试，会非常有趣！
I have a ball sticking balloons on the kids who come to my public lectures. I have done this for years at kids’ birthday parties, and you can have great fun with it too!
感应效应适用于各种物体，包括导体和绝缘体。你可以用那种在杂货店或一元店就能买到的充氦铝箔气球来做梳子实验。当你把梳子靠近气球时，气球上的自由电子会远离带负电的梳子，留下带正电的离子靠近梳子，这些离子会吸引气球靠近梳子。
Induction works for all kinds of objects, conductors as well as insulators. You could do the comb experiment with one of those helium-filled Aluminized Mylar balloons you can buy in grocery or dollar stores. As you bring the comb near the balloon, its free electrons tend to move away from the negatively charged comb, leaving positively charged ions nearer the comb, which then attract the balloon toward it.
虽然我们可以用头发或衣服摩擦橡胶气球使其带电，但实际上，橡胶几乎是一种理想的绝缘体——这也是它被用来包裹导线的原因。橡胶可以防止电荷从导线泄漏到潮湿的空气中，或跳到附近的物体上产生火花。毕竟，你肯定不希望火花在易燃环境中乱窜，比如你家的墙壁。橡胶一直以来都能保护我们免受电击。然而，它却无法保护我们免受最强大的静电——闪电的侵害。不知为何，人们总是反复强调橡胶运动鞋或橡胶轮胎可以防雷的说法。我不明白为什么这种说法至今仍然流传，但你最好立刻忘记它们！闪电威力巨大，根本不会在意一小块橡胶。当然，如果闪电击中你的汽车，你或许会安全——但实际上很可能并非如此——但这与橡胶轮胎没有任何关系。稍后我会详细解释这一点。
Even though we can charge rubber balloons by rubbing them on our hair or shirt, rubber is, in fact, a nearly ideal insulator—which is why it’s used to coat conducting wires. The rubber keeps charge from leaking out of the wires into moist air or jumping to a nearby object—making sparks. After all, you don’t want sparks jumping around in flammable environments, like the walls of your house. Rubber can and does protect us from electricity all the time. What it cannot do, however, is protect us from the most powerful form of static electricity you know: lightning. For some reason people keep repeating the myth that rubber sneakers or rubber tires can protect us from lightning. I’m not sure why these ideas still have any currency, but you’re best off forgetting them immediately! A lightning bolt is so powerful that it doesn’t care one bit about a little bit of rubber. Now you may be safe if lightning hits your car—probably not, in reality—but it doesn’t have anything to do with the rubber tires. I’ll get to that a little later.
电场和火花
Electric Fields and Sparks
我之前说过，闪电只不过是一个巨大的火花，一个复杂的火花，但仍然是火花。那么你可能会问，火花究竟是什么呢？好吧，要理解火花，我们需要了解一些关于电荷的重要知识。所有电荷都会产生看不见的电场，就像所有物体都会产生看不见的引力场一样。当你把带相反电荷的物体靠近时，你会看到它们之间的吸引力；或者，当你把带相同电荷的物体靠近时，你会看到它们之间的斥力——你看到的正是物体之间电场的作用。
I said before that lightning was just a big spark, a complicated spark, but still a spark. But then what, you may ask, are sparks? OK, to understand sparks we need to understand something really important about electric charge. All electric charges produce invisible electric fields, just as all masses produce invisible gravitational fields. You can sense the electric fields when you bring oppositely charged objects close to each other and you see the attraction between them. Or, when you bring like-charged objects close and see the repelling force—you are seeing the effects of the electric field between the objects.
我们用伏特每米来测量电场强度。坦白说，解释伏特是什么并不容易，更别提伏特每米了，但我会尝试解释一下。物体的电压是衡量其电势的指标。我们将地球的电势设为零。因此，地球的电压为零。带正电物体的电压为正值；它被定义为将一个单位正电荷（+1库仑——大约相当于6×10¹⁸个质子的电荷）从地球或任何与地球相连的导电物体（例如，你家里的水龙头）移动到该物体上所需的能量。为什么我需要产生能量来移动这个单位电荷呢？回想一下，如果该物体带正电，它会排斥这个单位正电荷。因此，我必须产生能量（在物理学中，我们称之为做功）来克服这种排斥力。能量的单位是焦耳。如果我需要产生 1 焦耳的能量，那么该物体的电势为 +1 伏。如果我需要产生 1000 焦耳的能量，那么电势为 +1000 伏。（关于 1 焦耳的定义，请参见第 9 章。）
We measure the strength of that field in units of volts per meter. Frankly, it’s not easy to explain what a volt is, let alone volts per meter, but I’ll give it a try. The voltage of an object is a measure of what’s called its electric potential. We will assign a zero electric potential to the Earth. Thus the Earth has zero voltage. The voltage of a positively charged object is positive; it’s defined as the amount of energy I have to produce to bring the positive unit of charge (+1 coulomb—which is the charge of about 6 × 1018 protons) from Earth or from any conducting object connected with the Earth (e.g., the water faucets in your house) to that object. Why do I have to produce energy to move that unit of charge? Well, recall that if that object is positively charged, it will repel the positive unit charge. Thus I have to generate energy (in physics we say I have to do work) to overcome that repelling force. The unit of energy is the joule. If I have to generate 1 joule’s worth of energy, then the electric potential of that object is +1 volt. If I have to generate 1,000 joules, then the electric potential is +1,000 volts. (For the definition of 1 joule, see chapter 9.)
如果物体带负电呢？那么它的电势为负值，电势定义为将单位负电荷（-1库仑，约6×10¹⁸个电子）从地球移动到该物体所需的能量。如果该能量为150焦耳，那么该物体的电势为-150伏。
What if the object is negatively charged? Then its electric potential is negative and it is defined as the energy I have to produce to move the negative unit of charge (–1 coulomb—about 6 × 1018 electrons) from the Earth to that object. If that amount of energy is 150 joules, then the electric potential of the object is –150 volts.
因此，伏特是电势的单位。它以意大利物理学家亚历山德罗·伏特的名字命名，伏特于1800年发明了第一个电化学电池，也就是我们现在所说的蓄电池。需要注意的是，伏特不是能量单位；它是单位电荷所含能量的单位（焦耳/库仑）。
The volt is therefore the unit of electric potential. It is named after the Italian physicist Alessandro Volta, who in 1800 developed the first electric cell, which we now call a battery. Note that a volt is not a unit of energy; it is a unit of energy per unit charge (joules/coulomb).
电流从高电势流向低电势。电流的大小取决于电势差和两个物体之间的电阻。绝缘体的电阻非常高；金属的电阻很低。电压差越大，电阻越小，产生的电流就越大。在美国，墙壁插座上两个小插槽之间的电势差为120伏（欧洲为220伏）；然而，这种电流是交流电（我们将在下一章讨论交流电）。电流的单位是安培（amp），以法国数学家和物理学家安德烈-玛丽·安培的名字命名。如果导线中的电流为1安培，则意味着每秒钟有1库仑的电荷通过导线。
An electric current runs from a high electric potential to a lower one. How strong this current is depends on the difference in electric potential and on the electric resistance between the two objects. Insulators have a very high resistance; metals have a low resistance. The higher the voltage difference and the lower the resistance, the higher the resulting electric current. The potential difference between the two small slots in the electric wall outlets in the United States is 120 volts (it’s 220 volts in Europe); however, that current is also alternating (we’ll get to the matter of alternating current in the next chapter). We call the unit of current the ampere (amp), named after the French mathematician and physicist André-Marie Ampère. If a current in a wire is 1 amp, it means that everywhere through the wire a charge of 1 coulomb passes per second.
那么火花呢？这一切又如何解释火花的产生？如果你经常用鞋子在地毯上摩擦，那么你和大地之间，或者你和6米外的金属门把手之间，可能已经积累了高达3万伏的电势差。这是3万伏电压乘以6米的距离，也就是每米5000伏。如果你靠近门把手，你和门把手之间的电势差不会改变，但距离会变小，因此电场强度会增强。很快，当你即将接触门把手时，大约1厘米的距离上就会达到3万伏的电势差。这相当于每米大约300万伏。
So what about sparks? How does all of this explain them? If you have scuffed your shoes a lot on the carpet, you may have built up an electric potential difference as high as about 30,000 volts between you and the Earth, or between you and the doorknob of a metal door 6 meters away from you. This is 30,000 volts over a distance of 6 meters, or 5,000 volts per meter. If you approach the doorknob, the potential difference between you and the doorknob will not change, but the distance will get smaller, thus the electric field strength will increase. Soon, as you are about to touch the doorknob, it will be 30,000 volts over a distance of about 1 centimeter. That’s about 3 million volts per meter.
在如此高的电场强度下（干燥空气中，1个大气压），就会发生我们所说的电击穿。电子会自发地跃入1厘米的间隙，并在此过程中电离空气。这反过来又会引发更多电子跃迁，最终导致雪崩式放电，产生火花！在你触碰到门把手之前，电流就已经通过空气传导到你的手指上了。我敢打赌，你现在肯定有点害怕，想起了上次被电到的那种感觉。真是痛快淋漓。你感觉到的火花，是因为电流引起你的神经快速而不舒服地收缩。
At this high value of the electric field (in dry air at 1 atmosphere) there will be what we call an electric breakdown. Electrons will spontaneously jump into the 1-centimeter gap, and in doing so will ionize the air. This in turn creates more electrons making the leap, resulting in an avalanche, causing a spark! The electric current shoots through the air to your finger before you can touch the doorknob. I’ll bet you’re cringing a bit, remembering the last time you felt such a lovely little shock. The pain you feel from a spark occurs because the electric current causes your nerves to contract, quickly and unpleasantly.
触电时发出的噼啪声是什么产生的？这很简单。电流会迅速加热空气，产生微小的压力波，也就是声波，这就是我们听到的声音。但火花也会产生光——尽管你可能在白天看不到光，但有时确实能看到。光的产生过程稍微复杂一些。当空气中产生的离子与电子重新结合，并将部分能量以光的形式释放出来时，就会产生光。即使你看不到火花发出的光（因为你不在黑暗的房间里对着镜子），在非常干燥的天气里梳头时，你也能听到它们发出的噼啪声。
What makes the noise, the crackle, when you get a shock? That’s easy. The electric current heats the air super quickly, which produces a little pressure wave, a sound wave, and that’s what we hear. But sparks also produce light—even though you may not see the light during the day, though sometimes you do. How the light is produced is a little more complicated. It results when the ions created in the air recombine with electrons in the air and emit some of the available energy as light. Even if you cannot see the light from sparks (because you aren’t in front of a mirror in a dark room), when you brush your hair in very dry weather you can hear the crackling noise they make.
想想看，即使你不费吹灰之力，只是梳梳头发或者脱掉那件涤纶衬衫，你的发梢和衬衫表面就会产生每米约300万伏的电场。所以，如果你伸手去摸门把手，感觉在3毫米处有火花，那么你和门把手之间的电位差就达到了1万伏左右。
Just think, without even trying very hard, by brushing your hair or taking off that polyester shirt, you have created, at the ends of your hair, and on the surface of your shirt, electric fields of about 3 million volts per meter. So, if you reach for a doorknob and feel a spark at, say, 3 millimeters, then the potential difference between you and the knob was of the order of 10,000 volts.
这听起来可能很多，但大多数静电其实并不危险，主要是因为即使电压很高，电流（单位时间内通过你的电荷量）也很小。如果你不介意轻微的电击，可以做一些电击实验，既能获得乐趣，又能同时演示物理原理。但是，千万不要把任何金属插入家里的电源插座。这样做非常非常危险——甚至会危及生命！
That may sound like a lot, but most static electricity isn’t dangerous at all, mainly because even with very high voltage, the current (the number of charges going through you in a given period of time) is tiny. If you don’t mind little jolts, you can experiment with shocks and have some fun—and demonstrate physics at the same time. However, never stick any metal in the electric outlets in your house. That can be very very dangerous—even life threatening!
尝试用聚酯纤维摩擦皮肤来给自己充电（记得穿橡胶底鞋或拖鞋，以免电荷泄漏到地板上）。关掉灯，然后慢慢地将手指靠近金属灯具或门把手。在它们接触之前，你应该能看到手指和金属之间有火花划过。你给自己充电越多，你和门把手之间产生的电压差就越大，火花就越强，声音也越大。
Try charging yourself up by rubbing your skin with polyester (while wearing rubber-soled shoes or flip-flops, so the charge doesn’t leak to the floor). Turn off the light and then slowly move your finger closer and closer to a metal lamp or doorknob. Before they touch you ought to see a spark jump across the air between the metal and your finger. The more you charge yourself up, the greater the voltage difference you’ll create between you and the doorknob, so the stronger the spark will be, and the louder the noise.
我的一位学生总是无意中给自己充电。他说他有一件涤纶浴袍，只在冬天穿。结果证明这是个糟糕的选择，因为每次脱下浴袍，他都会给自己充电，然后在关掉床头灯时被电到。原来，人体皮肤是摩擦电序列中最正的材料之一，而涤纶是最负的材料之一。所以，如果你想在黑暗的房间里对着镜子观察火花四溅的现象，最好穿涤纶衬衫，而不是涤纶浴袍。
One of my students was charging himself up all the time without meaning to. He reported that he had a polyester bathrobe that he only wore in the wintertime. This turned out to be an unfortunate choice, because every time he took the robe off, he charged himself up and then got a shock when he turned off his bedside lamp. It turns out that human skin is one of the most positive materials in the triboelectric series, and polyester is one of the most negative. This is why it’s best to wear a polyester shirt if you want to see the sparks flying in front of a mirror in a dark room, but not a polyester bathrobe.
为了用一种颇为戏剧化（也十分滑稽）的方式演示人是如何带电的，我请一位穿着涤纶外套的学生坐在教室前面的塑料椅子上（塑料是极好的绝缘体）。然后，我站在一块玻璃板上，以隔绝地面，开始用猫毛抽打这位学生。在学生们的哄堂大笑中，我持续抽打了大约半分钟。由于电荷守恒定律，我和这位学生会分别带上相反的电荷，并在我们之间建立起电势差。我向全班同学展示了我手里拿着一根霓虹灯管的一端。然后我们关掉了教室里的灯，在完全黑暗的环境下，我用灯管的另一端触碰这位学生，一道闪光过后（我们俩都感觉到了电击）！我和这位学生之间的电势差至少有3万伏。流经霓虹灯管和我们身体的电流使我们俩都释放了电荷。这个演示既滑稽又非常有效。
To demonstrate in a rather dramatic (and very funny) way how people can get charged, I invite a student who is wearing a polyester jacket to sit on a plastic chair in front of the class (plastic is an excellent insulator). Then, while standing on a glass plate to insulate myself from the floor, I start beating the student with cat fur. Amid loud laughter of the students, the beating goes on for about half a minute. Because of the conservation of charge, the student and I will get oppositely charged, and an electric potential difference will build up between us. I show my class that I have one end of a neon flash tube in my hand. We then turn off the lights in the lecture hall, and in complete darkness I touch the student with the other end of the tube, and there is a light flash (we both feel an electric shock)! The potential difference between the student and me must have been at least 30,000 volts. The current flowing through the neon flash tube and through us discharged both of us. The demonstration is hilarious and very effective.
YouTube 上的“教授殴打学生”视频展示了我讲课时殴打学生的片段：www.organic-chemistry.com/videos-professor-beats-student-%5BP4XZ-hMHNuc%5D.cfm。
“Professor Beats Student” on YouTube shows the beating part of my lecture: www.organic-chemistry.com/videos-professor-beats-student-%5BP4XZ-hMHNuc%5D.cfm.
为了进一步探索电势的奥秘，我使用了一种名为范德格拉夫起电机的奇妙装置。它看起来像是一个简单的金属球，安装在一个圆柱体上。实际上，它是一种能够产生巨大电势的巧妙装置。我教室里的那台通常能产生大约30万伏的电压——但它们可以达到更高的电压。如果你查看我网站上的前六节课，就会发现这一点。在电磁学课程（8.02）中，你会看到我用范德格拉夫起电机做的一些滑稽的演示。你会看到我制造电场击穿——范德格拉夫起电机的大圆顶和一个接地的小球（因此与地球相连）之间会产生巨大的火花。你会看到一个看不见的电场如何点亮荧光灯管，你会看到当灯管垂直于电场时，它就会“熄灭”。你甚至会看到，在完全黑暗的环境下，我（短暂地）触碰灯管的一端，与地线形成回路，灯管的亮度反而更高了。我忍不住叫了一声，因为电击的力度确实相当大，尽管它一点也不危险。如果你想（和我的学生一样）体验真正的惊喜，请观看第六讲的结尾，我会演示拿破仑令人震惊的沼气检测方法。网址是：http ://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/ 。
To further explore the mysteries of electric potential I use a wonderful device known as the Van de Graaff generator, which appears to be a simple metal sphere mounted on a cylindrical column. In fact, it’s an ingenious device for producing enormous electric potentials. The one in my classroom generally tops out at about 300,000 volts—but they can go much higher. If you look at the first six lectures on the web in my electricity and magnetism course (8.02), you will see some of the hilarious demonstrations I can do with the Van de Graaff. You’ll see me create electric field breakdown—huge sparks between the large dome of the Van de Graaff and a smaller grounded ball (thus connected with the Earth). You’ll see the power of an invisible electric field to light a fluorescent tube, and you’ll see that when the tube turns perpendicular to the field it turns “off.” You’ll even see that in complete darkness I (briefly) touch one end of the tube, making a circuit with the ground, and the light glows even more strongly. I cry out a little bit, because the shock is actually pretty substantial, even though it’s not in the least bit dangerous. And if you want a real surprise (along with my students), see what happens at the end of lecture 6, as I demonstrate Napoleon’s truly shocking method of testing for swamp gas. The URL is: http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/.
幸运的是，高压电本身不会致命，甚至不会造成伤害。真正重要的是流经你身体的电流。电流是指单位时间内通过的电荷量，正如前面提到的，我们用安培来测量它。电流，尤其是持续电流，会真正造成伤害甚至致命。为什么电流如此危险？最简单的原因是，流经你身体的电荷会引起肌肉收缩。在极低的电流水平下，肌肉能够收缩，或者说“活动”，这对于我们正常活动至关重要。但在高电流水平下，它会导致肌肉和神经过度收缩，以至于无法控制地抽搐，并伴有疼痛。在更高的电流水平下，甚至会导致心脏停止跳动。
Fortunately, high voltage alone won’t kill or even injure you. What counts is the current that goes through your body. Current is the amount of charge per unit of time, and as said before, we measure it in amperes. It’s current that can really hurt or kill you, especially if it’s continuous. Why is current dangerous? Most simply, because charges moving through your body cause your muscles to contract. At extremely low levels, electric currents make it possible for your muscles to contract, or “fire,” which is vital to getting around in life. But at high levels, it causes your muscles and nerves to contract so much that they twitch uncontrollably, and painfully. At even higher levels, it causes your heart to stop beating.
正因如此，电力与人体历史中较为黑暗的一面便是利用电力进行酷刑——因为它能造成难以忍受的痛苦——当然，在电椅的情况下，最终会导致死亡。如果你看过电影《贫民窟的百万富翁》，或许还记得警局里那些骇人的酷刑场景：残暴的警察将电极连接到年轻的贾马尔身上，导致他身体剧烈抽搐。
It is for these reasons that one of the darker sides of the history of electricity and the human body is the use of electricity for torture—since it can cause unbearable pain—and death, of course, in the case of the electric chair. If you’ve seen the movie Slumdog Millionaire, you may remember the horrible torture scenes in the police station, in which the brutish police attach electrodes to the young Jamal, causing his body to twitch wildly.
低强度电流实际上可能对健康有益。如果您曾经接受过背部或肩部的物理治疗，您可能体验过治疗师所说的“电刺激”（简称“电刺激”）。他们会将连接电源的导电贴片贴在受影响的肌肉上，并逐渐增加电流。您会有一种奇特的感觉，感觉肌肉在没有任何自主活动的情况下收缩和放松。
At lower levels, current can actually be healthy. If you’ve ever had physical therapy for your back or shoulder, you may have had the experience of what the therapists call “electrical stimulation”—stim for short. They put conducting pads connected to an electrical power source on the affected muscle and gradually increase the current. You have the odd sensation of feeling your muscles contract and release without your doing anything at all.
电力也被用于更戏剧性的治疗手段。你们都看过电视节目，里面用除颤器这种电极片来帮助心脏骤停的病人恢复心跳。去年我做心脏手术时，也曾出现过心脏骤停，医生们就是用除颤器帮我恢复了心跳——而且成功了！如果没有除颤器，《热爱物理》这本书可能永远都不会问世。
Electricity is also used in more dramatic healing efforts. You’ve all seen the TV shows where someone uses the electric pads, known as defibrillators, to try to regularize the heartbeat of a patient in cardiac distress. At one point in my own heart surgery last year, when I went into cardiac arrest, the doctors used defibrillators to get my heart beating again—and it worked! Without defibrillators, For the Love of Physics would never have seen the light of day.
人们对致命电流的确切数值存在分歧，原因显而易见：很少有人会进行危险电流强度的实验。而且，电流流经手部、大脑或心脏的情况也大相径庭。手部可能只会灼伤。但几乎所有人都认同，即使电流超过十分之一安培，持续时间不到一秒，如果流经心脏，也可能致命。电椅使用的电流强度似乎各不相同，电压约为2000伏，电流从5安培到12安培不等。
People disagree about the exact amount of current that’s lethal, for obvious reasons: there’s not too much experimenting with dangerous levels. And there’s a big difference as to whether the current passes through one of your hands, for instance, or whether it goes through your brain or heart. Your hand might just burn. But pretty much everyone agrees that anything more than a tenth of an ampere, even for less than a second, can be fatal if it goes through your heart. Electric chairs used varied amounts, apparently; around 2,000 volts and from 5 to 12 amperes.
你还记得小时候被叮嘱不要用刀叉去拿烤面包，以免触电吗？这是真的吗？我刚刚查看了我家三件电器的额定电流：收音机（0.5安培）、烤面包机（7安培）和咖啡机（7安培）。大多数电器底部都有标签标明电流。有些电器没有标明安培数，但你可以用功率（瓦特）除以电压（美国通常为120伏）来计算。我家的大多数断路器额定电流在15到20安培之间。你的120伏电器实际电流是1安培还是10安培其实并不重要。重要的是你要避免意外造成短路，以及……所有这些都可能导致触电，比如不小心用金属物体接触到120伏的电压；如果你刚洗完澡就这么做，可能会致命。那么，所有这些信息加起来意味着什么呢？很简单：你妈妈告诉你不要在烤面包机插着电的时候把刀插进去，她是对的。如果你想修理任何电器，一定要先拔掉电源。永远不要忘记，电流非常危险。
Remember when you were told as a kid not to put a fork or knife into a toaster in order to pull a piece of toast out, because you might electrocute yourself? Is that really true? Well, I just looked at the ratings of three appliances in my house: a radio (0.5 amp), my toaster (7 amps), and my espresso machine (7 amps). You can find these on a label on the bottom of most appliances. Some don’t have the amperage, but you can always calculate it by dividing the wattage, the appliance’s power, by the voltage, usually 120 in the United States. Most of the circuit breakers in my home are rated at between 15 and 20 amps. Whether your 120-volt appliances draw 1 or 10 amps is not really what matters. What matters is that you have to stay away from accidentally causing a short circuit and, above all, from accidentally touching with a metal object the 120 volts; if you did this shortly after you had taken a shower, it could kill you. So what does all this information add up to? Just this: when your mother told you not to put a knife into a toaster while it was plugged in, she was right. If you ever want to repair any of your electric appliances, make sure you unplug them first. Never forget that current can be very dangerous.
神圣火花
Divine Sparks
当然，最危险的电流之一就是闪电，它也是所有电现象中最引人注目的现象之一。它威力强大，难以预测，常被误解，而且充满神秘感。从希腊神话到玛雅神话，闪电既是神灵的象征，也是他们使用的武器。这不足为奇。地球上平均每年发生约1600万次雷暴，每天超过43000次，平均每小时约1800次，每秒产生约100次闪电，每天超过800万次闪电，遍布全球。
Of course, one of the most dangerous kinds of current is lightning, which is also one of the most remarkable of all electrical phenomena. It’s powerful, not completely predictable, much misunderstood, and mysterious, all at once. In mythologies from the Greek to the Mayan, lightning bolts have been either symbols of divine beings or weapons wielded by them. And no wonder. On average, there are about 16 million thunderstorms on Earth every year, more than 43,000 every day, roughly 1,800 every hour of the day, producing about 100 lightning flashes every second, or more than 8 million lightning flashes every day, scattered around our planet.
闪电是由于雷云带电而产生的。通常情况下，云的顶部带正电，底部带负电。至于为什么会这样，我们目前还没有完全理解。信不信由你，大气物理学中还有很多我们仍在学习的内容。现在，我们先简化一下，想象一朵云的负电荷位于靠近地球的一侧。由于感应作用，靠近云的地面会带正电，从而在地球和云之间产生电场。
Lightning happens when thunderclouds become charged. Generally the top of the cloud becomes positively charged, and the bottom becomes negative. Why this is the case is not yet completely understood. There’s a lot of atmospheric physics, believe it or not, that we are still learning. For now, we’ll simplify and imagine a cloud with its negative charge on the side closest to the Earth. Because of induction, the ground nearest the cloud will become positively charged, generating an electrical field between the Earth and the cloud.
闪电的物理原理相当复杂，但本质上，当云层与地面之间的电位差达到数千万伏时，就会发生闪电（电击穿）。虽然我们通常认为闪电是从云层射向地面，但实际上电流既可以从云层流向地面，也可以从地面流回云层。图中展示了一次普通闪电中的电流。闪电的电流约为5万安培（尽管有时可能高达几十万安培）。一次普通闪电的最大功率约为1万亿瓦（10¹²瓦）。然而，这种高功率持续时间仅为几十微秒。因此，每次闪电释放的总能量很少超过几亿焦耳。这相当于一个100瓦灯泡一个月消耗的能量。因此，收集闪电能量不仅不切实际，而且用途也不大。
The physics of a lightning strike is pretty complicated, but in essence a flash of lightning (electric breakdown) occurs when the electric potential between the cloud and Earth reaches tens of millions of volts. And though we think of a bolt as shooting from a cloud down to Earth, in truth they flow both from the cloud to the ground and from the ground back up to the cloud. Electric currents during an average lightning bolt are about 50,000 amps (though they can be as high as a few hundred thousand amps). The maximum power during an average lightning stroke is about a trillion (1012) watts. However, this lasts only for about a few tens of microseconds. The total energy released per strike is therefore rarely more than a few hundred million joules. This is equivalent to the energy that a 100-watt light bulb would consume in a month. Harvesting lightning energy is therefore not only impractical but also not too useful.
我们大多数人都知道，通过观察闪电和听到雷声之间的时间间隔，就能判断闪电的距离。但背后的原理却让我们得以窥见其中蕴含的强大力量。这与我曾经听一位学生解释的截然不同：他认为闪电会形成某种低压区，而雷声则是由空气涌入低压区并与另一侧的空气碰撞产生的。事实上，情况几乎恰恰相反。闪电的能量会将空气加热到约20000摄氏度，是太阳表面温度的三倍多。这种过热的空气会产生强大的压力波，冲击周围较冷的空气，从而产生声波，并在空气中传播。由于声波在空气中传播大约需要5秒，因此通过计算时间，就能比较容易地估算出闪电的距离。
Most of us know that we can tell how far away a lightning strike is by how much time elapses between seeing the bolt and hearing the thunder. But the reason why this is true gives us a glimpse of the powerful forces at play. It has nothing to do with the explanation I heard from a student once: that the lightning makes a low pressure area of some sort, and the thunder results from air rushing into the breach and colliding with the air from the other side. In fact, it’s almost exactly the reverse. The energy of the bolt heats the air to about 20,000 degrees Celsius, more than three times the surface temperature of the Sun. This superheated air then creates a powerful pressure wave that slams against the cooler air around it, making sound waves that travel through the air. Since sound waves in air travel about a mile in five seconds, by counting off the seconds you can figure out fairly easily how far away a lightning strike was.
闪电剧烈加热空气这一事实，也解释了你在雷暴中可能体验到的另一种现象。你是否注意到，在乡村雷雨过后，空气中弥漫着一种特殊的气味，一种清新的气息，仿佛暴雨洗涤了空气一般？在城市里很难闻到这种气味，因为那里总是充斥着汽车尾气。但即使你体验过这种美妙的香气——如果你还没有，我建议你下次雷雨过后在户外时仔细闻一闻——我敢打赌你也不知道，那是臭氧的味道，臭氧是由三个氧原子组成的氧分子。普通的无味氧分子由两个氧原子组成，我们称之为O₂ 。但是，闪电放电产生的巨大热量会将普通的氧分子分解——并非全部，但足以产生影响。而且这些单个氧原子本身不稳定，所以它们会附着在普通的O₂分子上，形成O₃——臭氧。
The fact that lightning bolts heat the air so dramatically explains another phenomenon you may have experienced in lightning storms. Have you ever noticed the special smell in the air after a thunderstorm in the country, a kind of freshness, almost as if the storm had washed the air clean? It’s hard to smell it in the city, because there’s always so much exhaust from cars. But even if you have experienced that wonderful fragrance—and if you haven’t I recommend you try to make note of it the next time you’re outdoors right after a lightning storm—I’ll bet you didn’t know that it’s the smell of ozone, an oxygen molecule made up of three oxygen atoms. Normal odorless oxygen molecules are made up of two oxygen atoms, and we call these O2. But the terrific heat of lightning discharges blows normal oxygen molecules apart—not all of them, but enough to matter. And these individual oxygen atoms are unstable by themselves, so they attach themselves to normal O2 molecules, making O3—ozone.
臭氧浓度低时气味宜人，但浓度过高时则令人不悦。高压输电线路下方经常会散发出臭氧。如果听到线路发出嗡嗡声，通常意味着线路中发生了电晕放电，也就是产生了臭氧。如果空气平静，你应该能闻到臭氧的气味。
While ozone smells lovely in small amounts, at higher concentrations it’s less pleasant. You can often find it underneath high-voltage transmission lines. If you hear a buzzing sound from the lines, it generally means that there is some sparking, what we call corona discharge, and therefore some ozone is being created. If the air is calm, you should be able to smell it.
现在让我们再来思考一下，穿运动鞋就能躲过雷击这种说法。一道电流高达5万到10万安培的闪电，足以将空气加热到太阳表面温度的三倍以上，几乎肯定会把你烧成焦炭，或者让你触电抽搐，或者瞬间将你体内的水分全部转化为超高温蒸汽，导致你爆炸——无论你穿不穿运动鞋。树木就是这样：树液爆裂，将树皮炸飞。一亿焦耳的能量——相当于大约50磅炸药的威力——这可不是小事。
Now let’s consider again the idea that you could survive a lightning strike by wearing sneakers. A lightning bolt of 50,000 to 100,000 amperes, capable of heating air to more than three times the surface temperature of the Sun, would almost surely burn you to a crisp, convulse you with electric shock, or explode you by converting all the water in your body instantaneously to superhot steam, sneakers or not. That’s what happens to trees: the sap bursts and blows off the tree’s bark. One hundred million joules of energy—the equivalent of about fifty pounds of dynamite—that’s no small matter.
那么，当闪电击中汽车时，橡胶轮胎是否真的能起到保护作用呢？你或许能暂时安全——当然，这并不能保证！——但这背后的原因却截然不同。电流会沿着导体的外侧流动，这种现象被称为趋肤效应。在汽车里，你实际上就坐在一个金属盒子里，而金属是良好的导体。你甚至可以触摸仪表盘的通风管道内部而不会受伤。然而，我强烈建议你不要这样做；这非常危险，因为现在大多数汽车都使用玻璃纤维部件，而玻璃纤维不具备趋肤效应。换句话说，如果闪电击中你的汽车，你和你的车都可能面临极其糟糕的后果。你可以看看以下网站上的短视频，视频中展示了闪电击中汽车的场景，以及一辆面包车被闪电击中后的照片：www.weatherimagery.com/blog/rubber-tires-protect-lightning/ 和 www.prazen.com/cori/van.html。显然，这绝非儿戏！
And what about whether you are safe inside a car when lightning strikes because of the rubber tires? You might be safe—no guarantees!—but for a very different reason. Electric current runs on the outside of a conductor, in a phenomenon called skin effect, and in a car you are effectively sitting inside a metal box, a good conductor. You might even touch the inside of your dashboard air duct and not get hurt. However, I strongly urge you not to try this; it is very dangerous as most cars nowadays have fiberglass parts, and fiberglass has no skin effect. In other words, if lightning strikes your car, you—and your car—could be in for an exceedingly unpleasant time. You might want to take a look at the short video of lightning striking a car and the photos of a van after having been hit by lightning at these sites: www.weatherimagery.com/blog/rubber-tires-protect-lightning/and www.prazen.com/cori/van.html. Clearly, this is not something to play around with!
幸运的是，对我们所有人来说，商业领域的情况截然不同。飞机。它们平均每年被闪电击中不止一次，但由于趋肤效应，它们往往能幸存下来。请观看此视频：www.youtube.com/watch?v =036hpBvjoQw 。
Fortunately for all of us, the situation is very different with commercial airplanes. They are struck by lightning on average more than once per year, but they happily survive because of the skin effect. Watch this video at www.youtube.com/watch?v=036hpBvjoQw.
关于闪电，还有一件事千万不要尝试，那就是本杰明·富兰克林那著名的实验：在雷雨天放风筝，风筝线上系着一把钥匙。据说，富兰克林想验证雷云会产生电火的假设。他推断，如果闪电真的是电的来源，那么一旦风筝线被雨水打湿，就会成为良好的导电体（尽管他没有使用“导电”这个词），电流会沿着风筝线流到系在风筝线末端的钥匙上。如果他把指关节靠近钥匙，应该能感觉到火花。然而，就像牛顿晚年声称自己是从树上掉下来的苹果中得到灵感一样，没有任何当时的证据表明富兰克林真的做过这个实验，只有他在写给英国皇家学会的一封信中提到过，以及十五年后他的朋友、氧气发现者约瑟夫·普里斯特利写的一封信中提到过。
Another thing not to try in regards to lightning is the experiment so famously attributed to Benjamin Franklin: flying a kite with a key attached to it during a thunderstorm. Supposedly, Franklin wanted to test the hypothesis that thunderclouds were creating electric fire. If lightning was truly a source of electricity, he reasoned, then once his kite string got wet from the rain, it should also become a good conductor of that electricity (though he didn’t use that word), which would travel down to the key tied at the base of the string. If he moved his knuckle close to the key, he should feel a spark. Now, as with Newton’s claim late in life to have been inspired by an apple falling to the ground out of a tree, there is no contemporary evidence that Franklin ever performed this experiment, only an account in a letter he sent to the Royal Society in England, and another one written fifteen years later by his friend Joseph Priestley, discoverer of oxygen.
无论富兰克林是否真的进行了这项实验——这项实验极其危险，很可能致命——他确实发表过一篇关于另一项实验的描述，该实验旨在通过在塔顶或尖顶放置一根长铁棒来将闪电引回地面。几年后，曾与富兰克林会面并将他的方案翻译成法语的法国人托马斯-弗朗索瓦·达利巴尔进行了一项略有不同的实验，并且活着回来了。他将一根40英尺长的铁棒竖立起来指向天空，并观察到铁棒底部（未接地）出现了火花。
Whether or not Franklin performed the experiment—which would have been fantastically dangerous, and very likely lethal—he did publish a description of another experiment designed to bring lightning down to earth, by placing a long iron rod at the top of a tower or steeple. A few years later, the Frenchman Thomas-François Dalibard, who had met Franklin and translated his proposal into French, undertook a slightly different version of the experiment, and lived to tell the tale. He mounted a 40-foot-long iron rod pointing up into the sky, and he was able to observe sparks at the base of the rod, which was not grounded.
出生于爱沙尼亚、当时居住在俄罗斯圣彼得堡的著名科学家格奥尔格·威廉·里希曼教授，是圣彼得堡科学院院士，他对电现象进行了深入研究。显然，他受到了达利巴德实验的启发，并决心尝试一下。根据迈克尔·布莱恩·希弗在其引人入胜的著作《引雷：本杰明·富兰克林与启蒙时代的电气技术》中的描述，他将一根铁棒固定在屋顶上。他把杆子拉到自己家，然后用黄铜链把杆子连接到一楼实验室里的电测量装置上。
Professor Georg Wilhelm Richmann, an eminent scientist born in Estonia then living in St. Petersburg, Russia, a member of the St. Petersburg Academy of Sciences who had studied electrical phenomena a good deal, was evidently inspired by Dalibard’s experiment, and determined to give it a try. According to Michael Brian Schiffer’s fascinating book Draw the Lightning Down: Benjamin Franklin and Electrical Technology in the Age of Enlightenment, he attached an iron rod to the roof of his house, and ran a brass chain from the rod to an electrical measuring device in his laboratory on the first floor.
真是巧合——或许是命运使然——1753年8月，在科学院的一次会议上，突然下起了雷暴。里奇曼匆匆赶回家，还带上了即将为他的新书绘制插图的画家。里奇曼正在检查设备时，一道闪电击中了他，沿着电线杆和链条向下窜，大约跳了一英尺就击中了里奇曼的头部，将他电击飞到房间另一边，同时闪电也击中了那位画家，使他昏迷过去。你可以在网上找到几幅描绘这一场景的插图，但尚不清楚这些插图是否出自那位画家之手。
As luck—or fate—would have it, during a meeting of the Academy of Sciences in August 1753, a thunderstorm developed. Richmann rushed home, bringing along the artist who was going to illustrate Richmann’s new book. While Richmann was observing his equipment, lightning struck, traveled down the rod and chain, jumped about a foot to Rich-mann’s head, electrocuted him and threw him across the room, while also striking the artist unconscious. You can see several illustrations of the scene online, though it’s not clear whether they were the creations of the artist in question.
富兰克林后来发明了一种类似的装置，但这种装置是接地的；我们今天称之为避雷针。它的确能有效地将雷击接地，但原因并非富兰克林最初设想的那样。他认为避雷针会在带电云层和建筑物之间产生持续放电，从而降低电位差，消除雷击的危险。他对自己的想法信心十足，甚至建议乔治二世国王在皇宫和弹药库上安装这种尖锐的装置。富兰克林的反对者则认为，避雷针只会吸引雷电，而放电降低建筑物和雷云之间电位差的效果微乎其微。据说，国王最终还是相信了富兰克林，安装了避雷针。
Franklin was to invent a similar contraption, but this one was grounded; we know it today as the lightning rod. It works well to ground lightning strikes, but not for the reason Franklin surmised. He thought that a lightning rod would induce a continuous discharge between a charged cloud and a building, thus keeping the potential difference low and eliminating the danger of lightning. So confident was he in his idea that he advised King George II to put these sharp points on the royal palace and on ammunition storage depots. Franklin’s opponents argued that the lightning rod would only attract lightning, and that the effect of the discharge, lowering the electric potential difference between a building and the thunderclouds, would be insignificant. The king, so the story goes, trusted Franklin and installed the lightning rods.
不久之后，一道闪电击中了其中一个弹药库，但损失却很小。所以避雷针确实起作用了，但原因却完全错误。富兰克林的批评者是对的：避雷针确实会吸引闪电，而且与雷云上巨大的电荷相比，避雷针的放电量确实微不足道。但避雷针真正起作用的原因是，如果它足够粗，能够承受1万到10万安培的电流，那么电流就会被限制在避雷针内，并将电荷转移到大地。富兰克林不仅才华横溢，而且运气也很好！
Not long thereafter a lightning bolt hit one of the ammunition depots, and there was very little damage. So the rod worked, but for completely the wrong reasons. Franklin’s critics were right: lightning rods do attract lightning, and the discharge of the rod is indeed insignificant compared to the enormous charge on the thundercloud. But the rod really works because, if it is thick enough to handle 10,000 to 100,000 amperes, then the current will stay confined to the rod, and the charge will be transferred to the earth. Franklin was not only brilliant—he was also lucky!
难道不令人惊奇吗？通过了解冬天脱毛衣时发出的细微沙沙声，我们也能对事物产生某种理解。是指能够照亮整个夜空的巨大雷暴，以及自然界中最响亮、最恐怖的声音之一的起源吗？
Isn’t it remarkable how by understanding the little crackle when we take off a sweater in winter, we can also come to some kind of understanding of the massive lightning storms that can light up the entire night sky, as well as the origin of one of the loudest, most terrifying sounds in all of nature?
在某些方面，我们仍然是现代版的本杰明·富兰克林，试图解开我们认知之外的谜团。20世纪80年代末，科学家们首次拍摄到发生在云层之上的闪电。其中一种被称为红色精灵闪电，由红橙色的放电组成，位于地球上方50至90公里处。此外，还有蓝色喷流，它们规模更大，有时长达70公里，直射高层大气。由于我们对它们的了解仅有二十余年，因此对于这些非凡现象的成因，我们仍然知之甚少。即使我们对电学了解颇多，每天大约45000次的雷暴中，仍然隐藏着许多真正的谜团。
In some ways we’re still latter-day versions of Benjamin Franklin, trying to figure out things beyond our understanding. In the late 1980s scientists first photographed forms of lightning that occur way, way above the clouds. One kind is called red sprites and consists of reddish orange electrical discharges, 50 to 90 kilometers above the earth. And there are blue jets as well, much larger, sometimes as much as 70 kilometers long, shooting into the upper atmosphere. Since we’ve only known about them for a little more than twenty years, there is an awful lot we don’t yet know about what causes these remarkable phenomena. Even with all we know about electricity, there are genuine mysteries on top of every thunderstorm, about 45,000 times a day.
第八章
CHAPTER 8
磁力的奥秘
The Mysteries of Magnetism
对我们大多数人来说，磁铁只是好玩的东西，部分原因是它们会产生我们可以感知和操控的力，同时这些力又是完全看不见的。当我们把两个磁铁靠近时，它们会像带电物体一样相互吸引或排斥。我们大多数人都觉得磁性与电有着密切的联系——例如，几乎所有对科学感兴趣的人都知道“电磁”这个词——但同样地，我们也无法确切地解释它们之间为什么或如何联系在一起。这是一个非常庞大的课题，我专门用一整门入门课程来讲解它，所以在这里我们只能浅尝辄止。即便如此，磁性的物理学原理也能很快地引导我们获得一些令人惊叹的效果和深刻的理解。
For most of us magnets are just fun, partly because they exert forces that we can feel and play with, and at the same time those forces are completely invisible. When we bring two magnets close together, they will either attract or repel each other, much as electrically charged objects do. Most of us have a sense that magnetism is deeply connected to electricity—nearly everyone interested in science knows the word electromagnetic, for instance—but by the same token we can’t exactly explain why or how they’re related. It’s a huge subject, and I spend an entire introductory course on it, so we’re just going to scratch the surface here. Even so, the physics of magnetism can lead us pretty quickly to some eye-popping effects and profound understandings.
磁场的奇妙之处
Wonders of Magnetic Fields
如果你拿一块磁铁，把它放在一台老式、非平板电视的电视机前面，当电视机开机时，你会看到屏幕上出现一些非常酷炫的图案和颜色。在液晶显示器（LCD）或等离子平板电视出现之前，电视机背面射出的电子束会形成这些图案和颜色。将物体靠近屏幕即可激活颜色，从而在屏幕上绘制图像。当你用强磁铁靠近这些屏幕时（就像我在课堂上演示的那样），屏幕上会出现近乎迷幻的图案。这些图案如此引人入胜，甚至连四五岁的孩子都喜欢。（你可以在网上轻松找到这些图案的图片。）
If you take a magnet and put it in front of an older, pre-flat-screen television when it’s turned on, you’ll see some very cool patterns and colors across the screen. In the days before liquid crystal display (LCD) or plasma flat screens, beams of electrons shooting from the back of the TV toward the screen activated the colors, effectively painting the image on the screen. When you take a strong magnet to one of these screens, as I do in class, it will make almost psychedelic patterns. These are so compelling that even four-and five-year-olds love them. (You can easily find images of these patterns online.)
事实上，孩子们似乎总是会自己发现这一点。焦虑的家长们在网上四处求助，请求帮助修复被孩子用冰箱磁铁在电视屏幕上刮蹭过的电视。幸运的是，大多数电视都配备了消磁装置，可以消除屏幕上的磁性，通常几天或几周后问题就会消失。但如果问题仍然存在，就需要请技术人员来修理了。因此，我不建议你把磁铁放在家里的电视屏幕（或电脑显示器）附近，除非你的电视或显示器是年代久远、你不在乎的。那样的话，你或许会觉得很有趣。世界知名的韩国艺术家白南准就用类似的方法创作了许多利用视频失真效果的艺术作品。在我的课堂上，我会打开电视，挑选一个特别糟糕的节目——广告是演示这个现象的绝佳素材——每个人都很喜欢磁铁彻底扭曲画面的效果。
In fact, children seem to discover this on their own all the time. Anxious parents are all over the web, pleading for help in restoring their TVs after their children have run refrigerator magnets across the screens. Fortunately, most TVs come with a degaussing device that demagnetizes screens, and usually the problem goes away after a few days or a few weeks. But if it doesn’t, you’ll need a technician to fix the problem. So I don’t recommend you put a magnet near your home TV screen (or computer monitor), unless it’s an ancient TV or monitor that you don’t care about. Then you might have some fun. The world-famous Korean artist Nam June Paik has created many works of art with video distortion in roughly the same way. In my class I turn on the TV and pick out a particularly awful program—commercials are great for this demonstration—and everyone loves the way the magnet completely distorts the picture.
就像电一样，磁的历史可以追溯到远古时代。两千多年前，希腊人、印度人和中国人似乎都知道，某些特定的岩石——后来被称为磁石——能够吸引细小的铁屑（就像希腊人发现摩擦琥珀会吸附树叶碎片一样）。如今，我们称这种物质为磁铁矿，一种天然存在的磁性矿物，事实上，它是地球上磁性最强的天然物质。磁铁矿是铁和氧的化合物（Fe₃O₄ ），因此也被称为氧化铁。
Just as with electricity, magnetism’s history goes back to ancient times. More than two thousand years ago the Greeks, the Indians, and the Chinese apparently all knew that particular rocks—which became known as lodestones—attracted small pieces of iron (just as the Greeks had found that rubbed amber would collect bits of leaves). Nowadays we call that substance magnetite, a naturally occurring magnetic mineral, in fact the most magnetic naturally occurring material on Earth. Magnetite is a combination of iron and oxygen (Fe3O4) and so is known as an iron oxide.
但磁铁种类繁多，并非只有磁铁矿。铁在磁性发展史上扮演了举足轻重的角色，并且至今仍是许多磁敏感材料的关键成分，因此，最易被磁铁吸引的材料被称为铁磁性材料（“铁”是表示铁的前缀）。这些材料通常是金属或金属化合物：当然包括铁本身，还有钴、镍和二氧化铬（曾大量用于磁带）。其中一些金属化合物可以通过置于磁场中永久磁化。另一些被称为顺磁性的物质，在磁场中会产生微弱的磁性，磁场消失后则恢复为非磁性。这些物质包括铝、钨、镁，以及（信不信由你）氧气。还有一些被称为抗磁性的物质，在磁场中会产生相当微弱的反向磁场。这类物质包括铋、铜、金、汞、氢和食盐，以及木材、塑料、酒精、空气和水。（某些物质具有铁磁性，某些物质具有顺磁性，而另一些物质具有抗磁性，这与电子在原子核周围的分布方式有关——这非常复杂，无法详细解释。）
But there are lots of different kinds of magnets, not only magnetite. Iron has played such a big role in the history of magnetism, and remains such a key ingredient of many magnetically sensitive materials, that those materials that are most attracted to magnets are called ferromagnetic (“ferro” is a prefix indicating iron). These tend to be metals or metal compounds: iron itself, of course, but also cobalt, nickel, and chromium dioxide (once used heavily in magnetic tapes). Some of these can be magnetized permanently by bringing them within a magnetic field. Other materials called paramagnetic become weakly magnetic when they’re placed in such a field and revert to being nonmagnetic when the field disappears. These materials include aluminum, tungsten, magnesium, and, believe it or not, oxygen. And some materials, called diamagnetic materials, develop fairly weak opposing magnetic fields in the presence of a magnetic field. This category includes bismuth, copper, gold, mercury, hydrogen, and table salt, as well as wood, plastics, alcohol, air, and water. (What makes certain materials ferromagnetic and some paramagnetic and others diamagnetic has to do with how the electrons are distributed around the nucleus—it’s much too complicated to go into in detail.)
甚至还有液态磁铁，它们并非严格意义上的铁磁性液体，而是铁磁性物质的溶液，能以非常奇妙的方式与磁铁产生反应。制作这种液态磁铁相当容易；这里有一个链接，里面有详细的制作说明：http ://chemistry.about.com/od/demonstrationsexperiments/ss/liquidmagnet.htm 。如果你把这种比较粘稠的溶液涂在一块玻璃上，然后在下面放一块磁铁，准备好迎接令人惊叹的结果吧——这比你在中学时看到的铁屑沿着磁力线排列要有趣得多。
There are even liquid magnets, which are not exactly ferromagnetic liquids, but rather solutions of ferromagnetic substances that respond to magnets in very beautiful and striking ways. You can make one of these liquid magnets fairly easily; here’s a link to a set of instructions: http://chemistry.about.com/od/demonstrationsexperiments/ss/liquidmagnet.htm. If you put this solution, which is fairly thick, on a piece of glass and put a magnet underneath, get ready for some remarkable results—a lot more interesting than watching iron filings line up along magnetic field lines as you may have seen in middle school.
十一世纪时，中国人似乎已经掌握了磁针的制作方法：将磁针接触磁铁矿，然后用丝线悬挂起来。这些磁针会沿着南北方向排列，与地球的磁力线保持一致。到了下一个世纪，指南针在中国乃至远至英吉利海峡的地方都被用于航海。当时的指南针由一根漂浮在水碗中的磁针组成。真是巧妙的设计！无论船只转向哪个方向，水碗都会转动，但磁针始终指向南北方向。
In the eleventh century, the Chinese seem to have magnetized needles by touching them to magnetite and then suspending them from a silk thread. The needles would align themselves in the north-south direction; they aligned themselves with the magnetic field lines of the Earth. By the following century, compasses were being used for navigation both in China and as far away as the English Channel. These compasses consisted of a magnetized needle floating in a bowl of water. Ingenious, wasn’t it? No matter which way the boat or ship turned, the bowl would turn but the needle would keep pointing north and south.
大自然的奇妙之处远不止于此。我们现在知道，迁徙的鸟类体内含有微小的磁铁矿，它们似乎利用这些磁铁矿作为内部指南针，帮助它们沿着迁徙路线飞行。一些生物学家甚至认为，地球磁场会刺激某些鸟类和其他动物（例如蝾螈）的视觉中枢，这表明在某种重要意义上，这些动物能够“看到”地球磁场。这真是太酷了！
Nature is even more ingenious. We now know that migrating birds have tiny bits of magnetite in their bodies that they apparently use as internal compasses, helping to guide them along their migration routes. Some biologists even think that the Earth’s magnetic field stimulates optical centers in some birds and other animals, like salamanders, suggesting that in some important sense, these animals can “see” the Earth’s magnetic field. How cool is that?
1600年，杰出的医生兼科学家威廉·吉尔伯特——他并非普通的医生，而是伊丽莎白一世女王的御医——出版了《论磁体、磁性物体以及地球》 （De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure）一书。书中他论证地球本身就是一块磁体，这一论证源于他用一种名为“地球仪”（terrella）的小型磁铁矿球体进行的实验。这种球体比葡萄柚略大一些，放置在其上的小型指南针的反应与放置在地球表面时完全相同。吉尔伯特声称，指南针指向北方是因为地球本身就是一块磁体，而不是像某些人认为的那样，是因为南北极存在磁岛，或者指南针指向北极星（Polaris）。
In 1600, the remarkable physician and scientist William Gilbert—not just any doctor, but physician to Queen Elizabeth I—published his book De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth), arguing that the Earth itself was a magnet, a result of his experiments with a terrella, a small magnetite sphere meant to be a model of the Earth. It was maybe a little larger than a grapefruit, and small compasses placed on it responded just as they did on the surface of the Earth. Gilbert claimed that compasses point north because the Earth was a magnet, not, as some thought, because there were magnetic islands at the North and South Poles, or that compasses were pointing toward Polaris, the North Star.
吉尔伯特不仅完全正确地指出地球拥有磁场，而且地球甚至还有磁极（就像冰箱贴的磁极一样），这些磁极并不与地理上的南北极完全重合。不仅如此，这些磁极还会进行一些漂移，每年大约移动15公里左右。因此，在某些方面，地球确实像一块简单的条形磁铁——一块普通的矩形磁性金属，你可以在模型店里买到——但在其他方面，地球又截然不同。科学家们花了很长时间才提出一个合理的理论来解释地球为什么会有磁场。地球核心含有大量铁这一事实并不足以解释磁场的存在，因为物体在超过一定温度（我们称之为居里温度）后就会失去铁磁性，铁也不例外；它的居里温度约为770摄氏度，而我们知道地核的温度远高于此！
Not only was Gilbert absolutely correct that the Earth has a magnetic field, but it even has magnetic poles (just like the poles in a refrigerator magnet), which do not quite coincide with the geographic north and south poles. Not only that, but these magnetic poles wander a bit, around 15 kilometers or so every year. So in some ways the Earth does act like a simple bar magnet—an ordinary rectangular magnetized piece of metal that you can buy in a hobby shop—but in other ways it’s completely different. It has taken scientists a very long time even to come up with a viable theory of why the Earth has a magnetic field. The fact that there’s a lot of iron in the Earth’s core isn’t enough, since above a certain temperature (we call it the Curie temperature) bodies lose their ferromagnetic quality, and iron is no exception; its Curie temperature is about 770° Celsius, and we know that the core is a whole lot hotter than that!
这个理论相当复杂，而且与电流有关。地球核心的循环以及地球的自转——物理学家称之为发电机效应。（天体物理学家利用发电机效应理论来解释恒星的磁场，包括我们太阳的磁场，太阳的磁场大约每11年就会完全反转一次。）这或许会让你感到惊讶，但科学家们仍在努力构建地球及其磁场的完整数学模型；可见地球磁场的复杂程度。更棘手的是，地质证据表明，地球磁场在数千年中发生了剧烈的变化：磁极的移动幅度远远超过了其年度周期，而且磁场似乎也发生了反转——仅在过去7000万年中就发生了150多次反转。真是不可思议，不是吗？
The theory is pretty involved, and has to do with the electric currents circulating in the Earth’s core and the fact that the Earth is rotating—physicists call this a dynamo effect. (Astrophysicists use the theory of these dynamo effects to explain magnetic fields in stars, including that of our own Sun, whose magnetic field completely reverses about every eleven years.) It may seem amazing to you, but scientists are still working on a full mathematical model of the Earth and its magnetic field; that’s how complex the field is. Their work is made even thornier by the fact that there’s geological evidence that the Earth’s magnetic field has changed dramatically over the millennia: the poles have traveled much more than their annual stroll, and it appears that the magnetic field has also reversed itself—more than 150 times over the last 70 million years alone. Wild stuff, isn’t it?
如今，借助配备高灵敏度磁力计的卫星（例如丹麦的奥斯特卫星），我们能够较为精确地绘制地球磁场图。由此可知，地球磁场延伸至太空超过一百万公里。我们也知道，在近地层中，磁场会引发大气层中最美丽的自然现象之一。
We are able to chart the Earth’s magnetic field with some exactness now, thanks to satellites (such as the Danish Ørsted satellite) equipped with sensitive magnetometers. From this we know that the magnetic field reaches more than a million kilometers out into space. We also know that closer to Earth, the magnetic field produces one of the more beautiful natural phenomena in our atmosphere.
你可能还记得，太阳会释放出一股巨大的带电粒子流，主要由质子和电子组成，被称为太阳风。地球磁场会将其中一些粒子引导到地球磁极附近的大气层中。当这些高速运动的粒子（平均速度约为每秒400公里）撞击大气中的氧气和氮气分子时，它们的一部分动能（运动能量）会转化为电磁能，以光的形式释放出来——氧气释放出绿色或红色光，氮气释放出蓝色或红色光。你可能已经猜到我要说什么了——没错：这就是造成壮观的极光现象的原因，在北半球被称为北极光，在南半球被称为南极光。为什么只有在极北或极南的地方才能看到这些光呢？因为太阳风主要在磁极附近进入地球大气层，那里的磁场最强。至于为什么有些夜晚的极光现象会更强烈……与其他情况相比，太阳耀斑爆发时会产生更多粒子，从而形成绚丽的极光。当发生巨大的太阳耀斑时，这些影响可能非常显著，引发我们所说的地磁暴，在远超正常区域的地方产生极光，有时还会干扰无线电传输、计算机运行、卫星运行，甚至造成停电。
The Sun, you may remember, emits a huge stream of charged particles, mostly protons and electrons, known as the solar wind. Earth’s magnetic field directs some of those particles down into our atmosphere at the magnetic poles. When these fast-moving particles, with average speeds of about 400 kilometers per second, bang into atmospheric oxygen and nitrogen molecules, some of their kinetic energy (energy of motion) gets transformed into electromagnetic energy in the form of light—oxygen releases green or red and nitrogen blue or red. You’re probably guessing where I’m going—that’s right: this is what produces the spectacular light show known as the aurora borealis, the northern lights, in the Northern Hemisphere and the aurora australis, or southern lights, in the Southern Hemisphere. Why do you only see these lights when you are very far north or very far south? Because the solar wind predominantly enters the Earth’s atmosphere near the magnetic poles, where the magnetic field is the strongest. The reason the effects are stronger on some nights than others is that whenever there are solar eruptions, there are more particles to make the light show. When there are huge solar flares, these effects can be massive, causing what we call geomagnetic storms, producing auroras far outside the normal areas and sometimes interfering with radio transmissions, computer functioning, satellite operations, and even causing power outages.
如果你不住在北极圈（或南极圈）附近，就很难看到极光。所以，如果你从美国东北部搭乘夜间航班前往欧洲（大多数航班都在晚上），不妨尽量选择飞机左侧的座位。因为飞机在七英里（约11公里）的高空，你或许能透过舷窗看到极光，尤其是在太阳活动特别活跃的时候（你可以在网上查到相关信息）。我就是这样多次看到极光的，所以只要有机会，我都会选择坐在飞机左侧。我想，在家随时都可以看电影。在飞机上，我晚上会寻找极光，白天则会寻找其他极光。
If you don’t live near the Arctic (or Antarctic) Circle, you won’t see these lights very often. That’s why, if you ever take an evening flight to Europe from the northeastern United States (and most flights are in the evening), you might want to try to get a seat on the left side of the plane. Since you’ll be seven miles up in the atmosphere, you might see some northern lights out your window, especially if the Sun has been particularly active recently, which you can find out online. I’ve seen it many times in just that way, so whenever I can, I sit on the left side of the plane. I figure I can watch movies whenever I want to at home. On planes I look for the northern lights at night and glories during the day.
我们确实应该感谢地球磁场，因为如果没有它，我们可能会遭受持续不断的带电粒子流冲击大气层的严重后果。太阳风很可能在数百万年前就吹走了我们的大气层和水，造成生命发展极其困难甚至不可能的环境。科学家推测，正是由于火星磁场较弱，太阳风的猛烈冲击才导致了这颗红色星球稀薄的大气层和相对缺乏水，在这种环境下，人类只有借助强大的生命维持系统才能生存。
We are truly indebted to Earth’s magnetic field, because without it, we might have suffered some serious consequences from the constant stream of charged particles bombarding our atmosphere. The solar wind might well have blasted away our atmosphere and water millions of years ago, creating conditions that would make the development of life much more difficult, if not impossible. Scientists theorize that just such a pounding by the solar wind due to Mars’s weak magnetic field is what accounts for the Red Planet’s thin atmosphere and comparative lack of water, an environment that human beings could inhabit only with the aid of powerful life support systems.
电磁学的奥秘
The Mystery of Electromagnetism
十八世纪，一些科学家开始怀疑电和磁之间存在某种联系——尽管另一些人，例如英国人托马斯·杨和法国科学家安德烈-玛丽·安培，则认为它们之间毫无关联。威廉吉尔伯特认为电和磁是完全不同的现象，但他仍然同时研究了这两种现象，并在《论磁体》一书中也论述了电。他将摩擦琥珀产生的吸引力称为“电力”（要知道，希腊语中琥珀的词是“ electron ”）。他甚至发明了一种验电器，这是测量和证明静电存在的最简单方法。（验电器的一根金属棒末端缠绕着一束金属丝。一旦带电，这些金属丝就会彼此分离：这相当于实验室里帽子上的“头发”效应。）
In the eighteenth century, a number of scientists began to suspect that electricity and magnetism were related in some way—even while others, such as the Englishman Thomas Young and the French scientist André-Marie Ampère, thought they had nothing to do with each other. William Gilbert thought that electricity and magnetism were completely separate phenomena, but he nevertheless studied both simultaneously and wrote about electricity in De Magnete as well. He called the attractive force of rubbed amber the “electric force” (remember, the Greek word for amber was “electron”). And he even invented a version of the electroscope, the simplest way to measure and demonstrate the existence of static electricity. (An electroscope has a bunch of tinsel strips at the end of a metal rod. As soon as it is charged, the strips stand out away from one another: the laboratory equivalent of hat hair.)
1776年和1777年，巴伐利亚科学院向学者征集关于电与磁关系的论文。人们早已知道闪电放电会使指南针失灵，而本杰明·富兰克林本人就曾利用莱顿瓶放电使磁针磁化。（莱顿瓶于19世纪中叶在荷兰发明，可以储存电荷，是如今我们称之为电容器的早期版本。）尽管19世纪初电学研究蓬勃发展，但直到丹麦物理学家汉斯·克里斯蒂安·奥斯特（生于1777年）做出将电与磁联系起来的关键发现之前，没有科学家能够清晰地将电流与磁联系起来。据历史学家弗雷德里克·格雷戈里称，这可能是现代物理学史上唯一一次在学生面前做出如此重大的发现。
The Bavarian Academy of Sciences invited essays on the relationship between electricity and magnetism in 1776 and 1777. People had known for some time that lightning discharges could make compasses go haywire, and none other than Benjamin Franklin himself had magnetized needles by using them to discharge Leyden jars. (Invented in the Netherlands at mid-century, the Leyden jar could store electric charges. It was an early version of the device we call a capacitor.) But while studies of electricity were exploding in the early nineteenth century, no scientist clearly linked electric current to magnetism until the Danish physicist Hans Christian Ørsted (born in 1777) made the absolutely crucial discovery bringing electricity and magnetism together. According to historian Frederick Gregory, this was probably the only time in the history of modern physics that such an enormous discovery was made in front of a class of students.
1820年，厄斯特注意到，当一根导线连接着电池时，电流会作用于附近的指南针，使其指向与导线垂直的方向，并偏离磁北和磁南方向。当他断开导线，切断电流后，指南针恢复了正常。厄斯特当时是否在讲课时有意进行这项实验，还是指南针恰巧就在手边，他只是观察到了这一惊人的现象，这一点尚不完全清楚。他自己的说法也前后矛盾——正如我们在物理学史上多次看到的那样。
Ørsted noticed, in 1820, that an electric current flowing through a wire that was connected to a battery affected a nearby compass needle, turning it in a direction perpendicular to the wire and away from magnetic north and south. When he disconnected the wire, cutting the current flow, the needle returned to normal. It’s not entirely clear whether Ørsted was conducting his experiment intentionally as part of a lecture, or whether the compass happened to be right at hand and he simply observed the astounding effect. His own accounts differ—as we’ve seen more than once in the history of physics.
无论这是一起意外还是蓄意行为，这或许就是……这是物理学家所进行过的最重要的实验（姑且这么称呼它）。他合理地得出结论：导线中的电流会产生磁场，而指南针中的磁针会随着这个磁场而移动。这一伟大的发现引发了十九世纪电磁学研究的爆发式增长，其中最著名的人物包括安德烈-玛丽·安培、迈克尔·法拉第、卡尔·弗里德里希·高斯，以及最终奠定基础的詹姆斯·克拉克·麦克斯韦的鸿篇巨制。
Whether it was an accident or purposeful, this may have been the most important experiment (let’s call it that) ever carried out by a physicist. He concluded reasonably that the electric current through the wire produced a magnetic field, and that the magnetic needle in the compass moved in response to that magnetic field. This magnificent discovery unleashed an explosion of research into electricity and magnetism in the nineteenth century, most notably by André-Marie Ampère, Michael Faraday, Carl Friedrich Gauss, and finally in the towering theoretical work of James Clerk Maxwell.
由于电流是由运动的电荷产生的，厄斯特证明了运动的电荷会产生磁场。1831年，迈克尔·法拉第发现，当他将一块磁铁穿过一个导电线圈时，线圈中会产生电流。实际上，他证明了厄斯特的论断——电流产生磁场——可以反过来成立：运动的磁场也会产生电流。但是，厄斯特和法拉第的发现都不符合直觉，对吧？如果你将一块磁铁靠近一个导电线圈（铜线圈效果很好，因为它导电性极佳），为什么线圈中会产生电流呢？起初，人们并不清楚这项发现的重要性。据说，不久之后，一位心存疑虑的政客问法拉第，他的发现是否有任何实际价值，而法拉第回答说：“先生，我不知道它有什么用。但是，有一点我可以肯定：总有一天，您会对它征税。”
Since current consisted of moving electric charges, Ørsted had demonstrated that moving electric charges create a magnetic field. In 1831 Michael Faraday discovered that when he moved a magnet through a conducting coil of wire, he produced an electrical current in the coil. In effect, he showed that what Ørsted had demonstrated—that electric currents produce a magnetic field—could be turned on its head: a moving magnetic field also produces electric currents. But neither Ørsted’s nor Faraday’s results make any intuitive sense, right? If you move a magnet near a conducting coil—copper works great because it’s so highly conductive—why on earth should you generate current in that coil? It wasn’t clear at first what the importance of this discovery was. Soon afterward, the story goes, a dubious politician asked Faraday if his discovery had any practical value, and Faraday is supposed to have responded, “Sir, I do not know what it is good for. However, of one thing I am quite certain; some day you will tax it.”
这种简单的现象，你在家就能轻松演示，或许听起来毫无道理，但毫不夸张地说，它支撑着我们整个经济体系和整个人类世界。如果没有这种现象，我们的生活方式可能还和十七、十八世纪的祖先差不多。我们会用蜡烛照明，没有收音机、电视、电话，也没有电脑。
This simple phenomenon, which you can easily demonstrate at home, may not make any sense at all, but without exaggeration, it runs our entire economy and the entire human-made world. Without this phenomenon we would still live more or less like our ancestors in the seventeenth and eighteenth centuries. We would have candlelight, no radio, no television, no telephones, and no computers.
我们今天使用的电力从何而来？总的来说，我们主要从发电站获取电力，而发电站则利用发电机产生电力。发电机最基本的工作原理是驱动铜线圈通过……磁场；我们不再移动磁铁。迈克尔·法拉第的第一个发电机是一个铜盘，他用曲柄将其固定在一个蹄形磁铁的两臂之间转动。铜盘外缘的电刷连接到一根导线，而旋转铜盘中心轴上的电刷连接到另一根导线。如果他将这两根导线连接到电流表，就能测量产生的电流。他投入系统的能量（人力！）通过他的装置转化为电能。但由于种种原因，这个发电机的效率并不高，其中一个主要原因是他必须用手转动铜盘。在某种程度上，我们应该称发电机为能量转换器。它们所做的只是将一种能量（在本例中是动能）转化为电能。换句话说，没有免费的午餐。（我将在下一章更深入地讨论能量转换。）
How do we get all this electricity that we use today? By and large we get it from power stations, which produce it with electric generators. Most fundamentally, what generators do is move copper coils through magnetic fields; we no longer move the magnets. Michael Faraday’s first generator was a copper disk that he turned with a crank between the two arms of a horseshoe magnet. A brush on the outer edge of the disk ran to one wire, and a brush on the central shaft of the turning disk ran to a second wire. If he hooked the two wires up to an ammeter, it would measure the current being generated. The energy (muscle power!) he put into the system was converted by his contraption into electricity. But this generator wasn’t very efficient for a variety of reasons, not the least of which was that he had to turn the copper disk with his hand. In some ways we ought to call generators energy converters. All they are doing is converting one kind of energy, in this case kinetic energy, into electric energy. There is, in other words, no free energy lunch. (I discuss the conversion of energy in more depth in the next chapter.)
电力转化为动力
Electricity into Motion
既然我们已经了解了如何将动能转化为电能，现在让我们来思考如何反过来，将电能转化为动能。汽车公司终于开始投入数十亿美元研发电动汽车，以实现这一目标。他们都在努力为这些汽车发明高效、强劲的电动机。那么，电动机是什么呢？电动机是将电能转化为动能的装置。它们都依赖于一个看似简单但实际上相当复杂的原理：如果你将一个通有电流的导电线圈置于磁场中，那么线圈就会趋向旋转。它的旋转速度取决于多种因素：电流强度、磁场强度、线圈形状等等。物理学家说，磁场会对导电线圈施加扭矩。“扭矩”是指使物体旋转的力。
Now that we’ve learned how to convert motion into electricity, let’s think about how to go in the other direction, converting electricity into motion. At long last, car companies are spending billions of dollars developing electric cars to do just that. They are all trying to invent efficient, powerful electric motors for these cars. And what are motors? Motors are devices that convert electric energy into motion. They all rely on a seemingly simple principle that’s pretty complicated in reality: if you put a conducting coil of wire (through which a current is running) in the presence of a magnetic field, then the coil will tend to rotate. How fast it rotates depends on a variety of factors: the strength of the current, the strength of the magnetic field, the shape of the coil, and the like. Physicists say that a magnetic field exerts a torque on a conducting coil. “Torque” is the term for a force that makes things rotate.
如果你换过轮胎，就能很容易地想象出扭矩的概念。你知道，这项工作最难的部分之一就是松开将车轮固定在车轴上的轮毂螺母。因为这些螺母通常……轮胎螺母拧得很紧，有时甚至感觉像冻住了一样，你需要用很大的力气才能拧松。轮胎扳手的手柄越长，所需的扭矩就越大。如果手柄特别长，你可能只需要轻轻一拧就能松开螺栓。更换备胎后，拧紧螺母时，你需要施加相反方向的扭矩。
You can visualize torque easily if you’ve ever changed a tire. You know that one of the most difficult parts of the operation is loosening the lug nuts holding the wheel onto the axle. Because these nuts are usually very tight, and sometimes they feel frozen, you have to exert tremendous force on the tire iron that grips the nuts. The longer the handle of the tire iron, the larger the torque. If the handle is exceptionally long, you may get away with only a small effort to loosen the bolts. You exert torque in the opposite direction when you want to tighten the nuts after you’ve replaced the flat tire with your spare.
当然，有时候无论你怎么用力推拉，螺母都纹丝不动。这种情况下，你可以喷点WD-40（出于这个原因以及其他很多原因，你应该始终在后备箱里备着WD-40），然后等一会儿让它松动；或者你可以试试用锤子敲击轮胎扳手的臂杆（这也是你应该始终随身携带的东西！）。
Sometimes, of course, no matter how hard you push or pull, you can’t budge the nut. In that case you either apply some WD-40 (and you should always carry WD-40 in your trunk, for this and many other reasons) and wait a bit for it to loosen, or you can try hitting the arm of the tire iron with a hammer (something else you should always travel with!).
我们无需在此深入探讨扭矩的复杂性。你只需知道，如果让电流流过线圈（例如使用电池），并将该线圈置于磁场中，线圈就会受到扭矩作用，并产生旋转的趋势。电流越大，磁场越强，扭矩也就越大。这就是直流电机的原理，而制作一个简单的直流电机也相当容易。
We don’t have to go into the complexities of torque here. All you have to know is that if you run a current through a coil (you could use a battery), and you place that coil in a magnetic field, a torque will be exerted on the coil, and it will want to rotate. The higher the current and the stronger the magnetic field, the larger the torque. This is the principle behind a direct current (DC) motor, a simple version of which is quite easy to make.
直流电和交流电究竟有什么区别？电池正负极的极性不会改变（正极始终是正极，负极始终是负极）。因此，如果你将电池连接到导线上，电流始终沿一个方向流动，这就是我们所说的直流电。然而，在美国，家用电源插座两端的电位差会以60赫兹的频率交替变化。在荷兰和欧洲大部分地区，频率为50赫兹。如果你将一根导线，例如白炽灯泡或加热线圈，连接到家里的插座上，电流会以60赫兹的频率振荡（即每秒反转120次）。这被称为交流电，简称AC。
What exactly is the difference between direct current and alternating current? The polarity of the plus and minus sides of a battery does not change (plus remains plus and minus remains minus). Thus if you connect a battery to a conducting wire, a current will always flow in one direction, and this is what we call direct current. At home (in the United States), however, the potential difference between the two openings of an electrical outlet alternate with a 60-hertz frequency. In the Netherlands and most of Europe the frequency is 50 hertz. If you connect a wire, say an incandescent lightbulb or a heating coil, to an outlet in your home, the current will oscillate (from one direction to the opposite direction) with a 60-hertz frequency (thus reversing 120 times per second). This is called alternating current, or AC.
每年在我的电磁学课上，我们都会举办电机竞赛。（这项竞赛是由我的同事和朋友维特·布沙教授和维克多·魏斯科普夫教授几年前首次举办的。）学生会收到一个信封，里面装着以下简单的材料：两米长的绝缘铜线、两个回形针、两个图钉、两块磁铁和一小块木头。他们需要自备一节1.5伏的AA电池。他们可以使用任何工具，可以切割木头和钻孔，但电机必须完全使用信封内的材料制作（不允许使用胶带或胶水）。任务是利用这些简单的材料制作一个转速尽可能快的电机（即每分钟转数最高）。回形针用来支撑旋转线圈，铜线用来制作线圈，磁铁的放置位置必须保证通电后能够对线圈施加扭矩。
Every year in my electricity and magnetism class we have a motor contest. (This contest was first done several years before me by my colleagues and friends Professors Wit Busza and Victor Weisskopf.) Each student receives an envelope with these simple materials: two meters of insulated copper wire, two paper clips, two thumbtacks, two magnets, and a small block of wood. They have to supply a 1.5-volt AA battery. They may use any tool, they may cut the wood and drill holes, but the motor must be built only of the material that is in the envelope (tape or glue is not allowed). The assignment is to build a motor that runs as fast as possible (produces the highest number of revolutions per minute, or RPMs) from these simple ingredients. The paper clips are meant to be the supports for the rotating coil, the wire is needed to make the coil, and the magnets must be placed so as to exert a torque on the coil when current from the battery goes through it.
假设你想参加比赛，当你把电池连接到线圈上时，线圈立刻开始顺时针旋转。到目前为止一切顺利。但或许你会惊讶地发现，线圈并没有持续旋转。原因是每旋转半圈，作用在线圈上的扭矩方向就会反转。扭矩反转会阻碍顺时针旋转；线圈甚至可能会短暂地逆时针旋转。显然，这不是我们想要的电机特性。我们想要的是电机持续朝一个方向旋转（无论是顺时针还是逆时针）。这个问题可以通过在每旋转半圈后反转流过线圈的电流方向来解决。这样，作用在线圈上的扭矩方向就始终保持不变，线圈也就能够持续朝该方向旋转。
Let’s assume you want to enter the contest, and that as soon as you connect the battery to your coil it starts to rotate in a clockwise direction. So far so good. But perhaps much to your surprise, your coil doesn’t keep rotating. The reason is that every half rotation, the torque exerted on your coil reverses direction. Torque reversal will oppose the clockwise rotation; your coil may even start to briefly rotate in the counterclockwise direction. Clearly, that’s not what we want from a motor. We want continuous rotation in one direction only (be it clockwise or counterclockwise). This problem can be solved by reversing the direction of the current through the coil after every half rotation. In this way the torque on the coil will always be exerted in the same direction, and thus the coil will continue to rotate in that one direction.
在制作电机时，我的学生必须应对扭矩反转这个不可避免的问题。一些学生设法制作了一个所谓的换向器，这种装置会在每旋转半圈后反转电流方向。但这很复杂。幸运的是，有一个非常巧妙且简单的解决方案，无需反转电流。如果能让电流（从而扭矩）在每旋转半圈后变为零，那么线圈在每次旋转的半圈内将完全不受扭矩作用，而在另一半圈内则始终受到方向相同的扭矩作用。最终结果是线圈会持续旋转。
In building their motors, my students have to cope with the inevitable problem of torque reversal, and a few students manage to build a so-called commutator, a device that reverses the current after every half rotation. But it’s complicated. Luckily there is a very clever and easy solution to the problem without reversing the current. If you can make the current (thus the torque) go to zero after every half rotation, then the coil experiences no torque at all during half of each rotation, and a torque that is always in the same direction during the other half of each rotation. The net result is that the coil keeps rotating.
学生每分钟每转一百圈，我就给他们加一分。电机最多可产生 20 分。学生们非常喜欢这个项目，而且因为他们是麻省理工学院的学生，这些年来他们设计出了许多令人惊叹的作品。你也想尝试一下。你可以点击 http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/lecture-notes/ 上的 PDF 链接，找到我第 11 讲的笔记，其中包含详细的说明。
I give a point for every hundred rotations per minute that a student’s motor produces, up to a maximum of twenty points. Students love this project, and because they are MIT students, they have come up with some amazing designs over the years. You may want to take a shot at this yourself. You can find the directions by clicking on the pdf link to my notes for lecture 11 at http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/lecture-notes/.
几乎所有学生都能比较轻松地制作出转速约为 400 转/分钟的电机。他们是如何保持线圈朝同一方向旋转的呢？首先，由于导线完全绝缘，他们必须刮掉线圈一端的绝缘层，使其始终与电池的一端接触——当然，选择哪一端都无所谓。真正棘手的是导线的另一端。学生们只希望电流在线圈旋转半圈内流过——换句话说，他们希望在半圈时断开电路。因此，他们刮掉导线另一端一半的绝缘层。这意味着导线圆周的一半是裸露的导线。在电流停止流动的时间段（每旋转半圈），即使没有扭矩作用，线圈也会继续旋转（摩擦力不足以使其在半圈内停止）。要掌握好刮擦技巧，并弄清楚哪一半的电线应该裸露，需要反复试验——但正如我所说，几乎任何人都能让它达到 400 转/分。我也是这么做的——但我自己始终无法让它超过 400 转/分。
Almost all students can make a motor that turns about 400 RPM fairly easily. How do they keep the coil turning in the same direction? First of all, since the wire is completely insulated, they have to scrape the insulation off one end of the wire coil so that it always makes contact with one side of the battery—of course, it does not matter which end they choose. It’s the other end of the wire that’s considerably trickier. Students only want the current to flow through the coil for half of its rotation—in other words, they want to break the circuit halfway through. So they scrape half of the insulation off of that other end of the wire. This means there’s bare wire for half of the circumference of the wire. During the times that the current stops (every half rotation), the coil continues to rotate even though there is no torque on it (there isn’t enough friction to stop it in half a rotation). It takes experimentation to get the scraping just right and to figure out which half of the wire should be bare—but as I said, nearly anyone can get it to 400 RPM. And that’s what I did—but I could never get much higher than 400 RPM myself.
后来一些学生告诉我我的问题所在。当线圈转速超过几百转/分时，它就会在支撑物（回形针）上振动，频繁地断开电路，从而中断扭矩输出。所以，比较聪明的学生想出了一个办法：用两根导线将线圈两端固定在回形针上，同时还能让线圈以最小的摩擦力旋转。你信不信，就这么一个小小的调整，他们竟然把转速提高到了4000转/分！
Then some students told me what my problem was. Once the coil starts turning more than a few hundred RPM, it starts to vibrate on its supports (the paper clips), breaking the circuit frequently, and therefore interrupting the torque. So the sharper students had figured out how to take two pieces of wire to hold the ends of the coil down on the paper clips at either end while still allowing it to rotate with little friction. And that little adjustment got them, believe it or not, to 4,000 RPM!
这些学生真是太有想象力了。几乎所有的电机，线圈的旋转轴线都是水平的。但有个学生却造了一台线圈旋转轴线垂直的电机。其中最好的一台转速达到了5200转/分——要知道，它竟然只靠一块1.5伏的小电池供电！我记得很清楚。获胜的学生是个大一新生。课后，他站在教室门口，和我站在一起，说道：“哦，莱文教授，这很简单。我大概十分钟就能给你造出一台转速4000转的电机。”说完，他就当着我的面把电机造出来了。
These students are so imaginative. In almost all motors, the axis of rotation of the coil is horizontal. But one student built a motor where the axis of rotation of the coil was vertical. The best one ever got up to 5,200 RPM—powered, remember by one little 1.5-volt battery! I remember the student who won. He was a freshman, and the young man said, as he stood with me after class in front of the classroom, “Oh, Professor Lewin, this is easy. I can build you a 4,000 RPM motor in about ten minutes.” And he proceeded to do it, right in front of my eyes.
但你无需尝试制作这种电机。有一种更简单的电机，只需几分钟就能用更少的元件制作完成：一块碱性电池、一小段铜线、一颗石膏板螺丝（或钉子）和一个小圆盘磁铁。它叫做单极电机。这里有详细的制作步骤说明和演示视频（如果你的电机转速超过 5000 转/分，请联系我）：www.evilmadscientist.com/article.php/HomopolarMotor
But you don’t need to try to create one of these. There’s an even simpler motor that you can make in a few minutes, with even fewer components: an alkaline battery, a small piece of copper wire, a drywall screw (or a nail), and a small disc magnet. It’s called a homopolar motor. There’s a step-by-step description of how to make one, and a video of one in action right here (drop me a line if yours goes faster than 5,000 RPM): www.evilmadscientist.com/article.php/HomopolarMotor.
与电机竞赛一样有趣，但方式截然不同的是，我在课堂上用一个直径1英尺的线圈和一个导电板进行的演示。正如你们现在所知，电流流过线圈会产生磁场。线圈中的交流电（AC）会产生交变磁场。（请记住，电池产生的电流是直流电。）由于我所在的教室的电频率是60赫兹的交流电，就像美国其他地方一样，因此线圈中的电流每1/120秒反转一次。如果我把这样的线圈放在一块金属板的正上方，变化的磁场（我称之为外部磁场）就会穿透导电板。根据法拉第电磁感应定律，这种变化的磁场会在金属板中产生电流；我们称之为涡流。涡流反过来又会产生变化的磁场。因此，将会出现两个磁场：外部磁场和涡流产生的磁场。
Just as much fun as the motor contest, in a totally different way, is another demonstration I perform in class with a 1-foot-diameter electric coil and a conducting plate. An electric current going through a coil will produce a magnetic field, as you now know. An alternating electric current (AC) in a coil will produce an alternating magnetic field. (Recall that the current created by a battery is a direct current.) Since the frequency of the electricity in my lecture hall is 60 hertz of alternating current, as it is everywhere in the United States, the current in my coil reverses every 1/120 second. If I place such a coil just above a metal plate, the changing magnetic field (I call this the external magnetic field) will penetrate the conducting plate. According to Faraday’s law, this changing magnetic field will cause currents to flow in the metal plate; we call these eddy currents. The eddy currents in turn will produce their own changing magnetic fields. Thus there will be two magnetic fields: the external magnetic field and the magnetic field produced by the eddy currents.
在1/60秒的周期中，大约有一半的时间里，两个磁场方向相反，线圈会被平板排斥；在另一半时间里，两个磁场方向相同，线圈会被平板吸引。由于一些相当微妙且过于技术性的原因（此处不赘述），线圈会受到一个净斥力，这个斥力足以使线圈悬浮。您可以在课程8.02第19讲的视频中看到这一点：http ://videolectures.net/mit802s02_lewin_lec19/ 。请观看讲座大约 44 分 20 秒处。
During about half the time in the 1/60-second cycle, the two magnetic fields are in opposite directions and the coil will be repelled by the plate; during the other half the magnetic fields will be in the same direction and the coil will be attracted by the plate. For reasons that are rather subtle, and too technical to discuss here, there is a net repelling force on the coil, which is strong enough to make the coil levitate. You can see this in the video for course 8.02, lecture 19: http://videolectures.net/mit802s02_lewin_lec19/. Look about 44 minutes and 20 seconds into the lecture.
我琢磨着我们应该能利用这种力使人悬浮起来，于是我决定像魔术师那样，用一个巨大的线圈让班上的一个女生躺在上面，然后让她悬浮起来。我和我的朋友马科斯·汉金和比尔·桑福德（物理演示小组的成员）努力让足够的电流流过线圈，但每次都把断路器烧断了。所以我们打电话给麻省理工学院的设施部门，告诉他们我们需要几千安培的电流，他们听了哈哈大笑。“我们得重新设计整个麻省理工学院才能给你们提供那么大的电流！”他们告诉我们。真是太可惜了，因为已经有好几个女生给我发邮件，表示愿意让我悬浮。我不得不一一回复，表示遗憾。但这并没有阻止我们，你可以登录观看大约47分半钟的讲座视频。我兑现了我的承诺；结果发现，这个女人比我原先预想的要轻得多。
I figured we ought to be able to harness this force to levitate a person, and I decided that I would levitate a woman in my class, just like magicians do, by creating a giant coil, having her lie on top, and levitating her. So my friends Markos Hankin and Bil Sanford (of the physics demonstration group) and I worked hard to get enough current going through our coils, but we ended up blowing the circuit breakers every time. So we called up the MIT Department of Facilities and told them what we needed—a few thousand amps of current—and they laughed. “We’d have to redesign MIT to get you that much current!” they told us. It was too bad, since a number of women had already emailed me, offering to be levitated. I had to write them all back with regrets. But that didn’t stop us, as you can see by logging on to the lecture at about 471/2 minutes in. I made good on my promise; the woman just turned out to be much lighter than I’d originally planned.
电磁力来帮忙
Electromagnetism to the Rescue
让女人悬浮起来的确是一个相当不错——也很有趣——的演示，但磁悬浮技术还有许多更令人惊叹、更有用的应用。它是许多新兴技术的基础，这些技术催生了世界上一些最酷炫、最快捷、污染最小的交通工具。
Levitating a woman makes for a pretty good—and funny—demonstration, but magnetic levitation has a host of more amazing and much more useful applications. It is the foundation of new technologies responsible for some of the coolest, fastest, least polluting transportation mechanisms in the world.
你可能听说过高速磁悬浮列车。许多人对它们着迷不已，因为它们似乎将无形的磁力与最流畅的现代空气动力学设计完美结合，并以极高的速度运行。你或许不知道“磁悬浮”的全称是“磁力悬浮”。但你肯定知道，当磁极靠近时，它们会相互吸引或排斥。磁悬浮列车的奇妙之处在于，如果能够找到控制这种吸引力或排斥力的方法，就应该能够让列车悬浮在轨道上方，然后通过控制其运行方向来控制列车的运行。高速列车。有一种采用电磁悬浮（简称EMS）技术的列车，利用列车上的电磁铁通过磁力吸引将其提升。列车底部有一个C形臂，上部与列车连接，下部位于轨道下方，其上表面装有磁铁，利用磁铁将列车提升到由铁磁性材料制成的轨道上。
You’ve probably heard of high-speed maglev trains. Many people find them utterly fascinating, since they seem to combine the magic of invisible magnetic forces with the sleekest of modern aerodynamic design, all moving at extremely high speeds. You may not have known that “maglev” stands for “magnetic levitation.” But you do know that when you hold magnetic poles close together, they either attract or repel each other. The wonderful insight behind maglev-trains is that if you could find a way to control that attractive or repulsive force, you ought to be able to levitate a train above tracks and then either pull or push it at high speed. For one kind of train, which works by electromagnetic suspension (known as EMS), electromagnets on the train lift it by magnetic attraction. The trains have a C-shaped arm coming down from them; the upper part of the arm is attached to the train, while the lower arm, below the track, has magnets on its upper surface that lift the train toward the rails, which are made of ferromagnetic material.
由于你不希望火车粘在铁轨上，而且这种吸引力本身就不稳定，所以需要一个复杂的反馈系统来确保火车与铁轨保持恰到好处的距离——这个距离不到一英寸！另一个独立的电磁铁系统通过同步开关来“拉动”火车前进，从而提供火车的推进力。
Since you don’t want the train to latch on to the rails, and since the attractive force is inherently unstable, a complicated feedback system is needed to make sure the trains remain just the right distance away from the rails, which is less than an inch! A separate system of electromagnets that switch on and off in synchronized fashion provide the train’s propulsion, by “pulling” the train forward.
另一种主要的磁悬浮列车系统是电动力悬浮（EDS），它利用磁斥力，并使用一种名为超导体的特殊装置。超导体是一种在极低温下电阻为零的物质。因此，由超导材料制成的超冷线圈只需极少的电能就能产生非常强的磁场。更令人惊奇的是，超导磁体可以像磁阱一样工作。如果将一块磁铁靠近它，重力和超导体之间的相互作用会将磁铁保持在特定的距离。因此，使用超导体的磁悬浮列车自然比电动力悬浮系统（EMS）稳定得多。如果你试图将超导体和磁铁推到一起或拉开，你会发现这非常困难。两者会倾向于保持彼此之间的距离。（这里有一个很棒的小视频演示了磁铁和超导体之间的关系：http://www.youtube.com/watch? v=nWTSzBWEsms 。）
The other main type of maglev train system, known as electro-dynamic suspension (EDS), relies on magnetic repulsion, using remarkable devices called superconductors. A superconductor is a substance that, when kept very cold, has no electric resistance. As a result, a supercooled coil made out of superconducting material takes very little electrical power to generate a very strong magnetic field. Even more amazing, a superconducting magnet can act like a magnetic trap. If a magnet is pushed close to it, the interplay between gravity and the superconductor holds the magnet at a particular distance. As a result, maglevs that use superconductors are naturally much more stable than EMS systems. If you try to push the superconductor and the magnet together or pull them apart, you’ll find it quite hard to do. The two will want to stay the same distance from each other. (There’s a wonderful little video that demonstrates the relationship between a magnet and a superconductor: http://www.youtube.com/watch?v=nWTSzBWEsms.)
如果底部装有磁铁的列车过于靠近装有超导体的轨道，增大的斥力会将其推开。如果列车距离轨道过远，重力又会将其拉回轨道。因此，列车车厢会悬浮在轨道上，保持平衡。与电磁悬浮系统（EMS）相比，列车前进主要依靠斥力，操作起来也更为简单。
If the train, which has magnets on the bottom, gets too close to the track, which has superconductors in it, the increased force of repulsion pushes it away. If it gets too far away, gravity pulls it back and causes the train to move toward the track. As a result, the train car levitates in equilibrium. Moving the train forward, which also uses mostly repulsive force, is simpler than in EMS systems.
两种方法各有优缺点，但都有效地解决了传统列车车轮摩擦的问题——这是造成磨损的主要原因之一——同时带来了更平稳、更安静、速度更快的乘坐体验。（它们仍然需要应对空气阻力问题，空气阻力会随着列车速度的增加而迅速增大。这就是为什么它们的设计如此符合空气动力学原理的原因。）上海磁悬浮列车采用电磁悬浮技术，于2004年开通运营，从市区到机场的19英里路程大约需要8分钟，平均时速（截至2008年）在139至156英里之间——尽管它的最高时速可达268英里，比世界上任何其他高速铁路都要快。您可以在这里观看由其制造商制作的上海磁悬浮列车的短片：www.youtube.com/watch? v=weWmTldrOyo 。磁悬浮列车有史以来的最高速度记录来自日本的一条试验轨道，JR磁悬浮列车在该轨道上达到了361英里/小时的速度。以下是关于这列日本列车的简短介绍：www.youtube.com/watch ?v=VuSrLvCVoVk&feature=related 。
Both methods have pluses and minuses, but both have effectively eliminated the problem of friction on conventional train wheels—a major component of wear and tear—while producing a far smoother, quieter, and above all faster ride. (They still have to cope with the problems of air drag, which increases rapidly with the speed of the train. That’s why they are designed to be so aerodynamically sleek.) The Shanghai Maglev Train, which works by means of electromagnetic suspension and opened in 2004, takes about 8 minutes to travel the 19 miles from the city to the airport, at an average speed (as of 2008) of between 139 and 156 miles per hour—though it’s capable of a top speed of 268 miles per hour, faster than any other high-speed railway in the world. You can see a short video of the Shanghai train here, made by its manufacturers: www.youtube.com/watch?v=weWmTldrOyo. The highest speed ever recorded on a maglev train belong to a Japanese test track, where the JR-Maglev train hit 361 miles per hour. Here’s a short piece on the Japanese train: www.youtube.com/watch?v=VuSrLvCVoVk&feature=related.
YouTube 上有很多既搞笑又内容丰富的磁悬浮技术视频。其中一个视频里，一个男孩用六块磁铁和一点橡皮泥让一支旋转的铅笔悬浮起来，你可以在家轻松复现这个实验：www.youtube.com/watch?v =rrRG38WpkTQ&feature =related。另外，还可以看看这个视频，它采用了超导设计。视频中，一节模型火车在轨道上飞驰，甚至还有一个简短的动画讲解：www.youtube.com/watch?v =GHtAwQXVsuk&feature=related 。
There are lots of hilarious and informative YouTube videos featuring maglev technology. This one, in which a boy levitates a spinning pencil with six magnets and a little modeling clay, features a demonstration you can reproduce easily at home: www.youtube.com/watch?v=rrRG38WpkTQ&feature=related. But also have a look at this one, using a superconductor design. It shows a model train car zipping around a track—and even has a little animated explanatory section: www.youtube.com/watch?v=GHtAwQXVsuk&feature=related.
不过，我最喜欢的磁悬浮演示是名为 Levitron 的奇妙小型旋转陀螺。您可以在www.levitron.com上看到不同的版本。我的办公室里就有一个早期的 Levitron，它已经让数百位访客赞叹不已。
My favorite Maglev demonstration, however, is the wonderful little spinning top known as the Levitron. You can see different versions at www.levitron.com. I have an early one in my office that has delighted hundreds of visitors.
磁悬浮列车系统确实具有环境优势——它们用电效率相对较高，而且不会排放温室气体。但磁悬浮列车并非无成本生产。因为大多数磁悬浮轨道与现有铁路不兼容。磁悬浮线路需要大量的初期投资，这阻碍了它们迄今为止的广泛商业应用。即便如此，如果我们不想毁灭地球，开发比我们今天使用的更高效、更清洁的公共交通系统对我们的未来至关重要。
Maglev train systems have genuine environmental advantages—they use electricity relatively efficiently and don’t emit greenhouse gases in exhaust. But maglev trains don’t produce something for nothing. Because most maglev tracks are not compatible with existing rail lines, maglev systems require a lot of up-front capital, which has worked against them being in widespread commercial use so far. Even so, developing more efficient and cleaner mass transit systems than what we use today is absolutely essential for our future if we’re not going to cook our own planet.
麦克斯韦的非凡成就
Maxwell’s Extraordinary Achievement
许多物理学家认为詹姆斯·克拉克·麦克斯韦是史上最重要的物理学家之一，或许仅次于牛顿和爱因斯坦。他对物理学的诸多领域都做出了卓越贡献，从土星环的分析到气体行为的研究、热力学以及颜色理论，无所不包。但他最辉煌的成就莫过于推导出了描述和联系电磁的四个方程，即著名的麦克斯韦方程组。这四个方程看似简单，但其背后的数学原理却相当复杂。如果您熟悉积分和微分方程，不妨观看我的讲座或上网搜索相关资料。为了便于理解，以下我们将用更简洁的方式介绍麦克斯韦的贡献。
Many physicists think that James Clerk Maxwell was one of the most important physicists of all time, perhaps right behind Newton and Einstein. He contributed to an incredible range of fields in physics, from an analysis of Saturn’s rings, to exploring the behavior of gases, thermodynamics, and the theory of color. But his most dazzling achievement was developing the four equations describing and linking electricity and magnetism that have become known as Maxwell’s equations. These four equations only appear simple; the math behind them is pretty complicated. But if you’re comfortable with integrals and differential equations, please take a look at my lectures or surf around on the web to learn about them. For our purposes, here’s what Maxwell did in simpler terms.
最重要的是，麦克斯韦统一了电磁理论，证明电磁现象本质上是同一种现象，只是表现形式不同。除了一个非常重要的例外，这四个方程并非他的“定律”或发明；它们早已以某种形式存在。然而，麦克斯韦的贡献在于将它们整合起来，形成了我们今天所说的完备场论。
Above all, Maxwell unified the theory of electricity and magnetism by showing these two phenomena to be just one phenomenon—electromagnetism—with different manifestations. With one very important exception, the four equations are not his “laws” or inventions; they already existed in one form or another. What Maxwell did, however, was bring them together in what we call a complete field theory.
第一个方程是高斯电学定律，它解释了电荷与它们产生的电场强度和分布之间的关系。第二个方程是高斯磁学定律，它是四个方程中最简单的，并且同时阐述了几个问题。它指出不存在磁单极子。磁铁总是具有南北极（我们称之为磁偶极子），而电则允许存在电单极子（单极子要么是带正电的粒子，要么是带负电的粒子）。如果你弄断一个如果你把冰箱上贴着很多磁铁，把它们分成两半，每半都有南北极；如果你把它们分成一万块，每块也都有南北极。你不可能一只手只拿着磁铁的北极，另一只手只拿着磁铁的南极。但是，如果你有一个带电物体（比如带正电的物体），把它分成两半，这两半都可能带正电。
The first of these equations is Gauss’s law for electricity, which explains the relationship between electric charges and the strength and distribution of the electric fields they create. The second equation, Gauss’s law for magnetism, is the simplest of the four and says several things at once. It says that there are no such things as magnetic monopoles. Magnets always have a north and south pole (we call them dipoles) as opposed to electricity which allows for electric monopoles (a monopole is either a positively charged particle or a negatively charged one). If you break one of your magnets (I have many on my refrigerator) in two pieces, each piece has a north and a south pole, and if you break it into 10,000 pieces, each has a north pole and a south pole. There is no way that you could end up with only a magnetic north pole in one hand and only a magnetic south pole in the other hand. However, if you have an object which is electrically charged (say, positively charged) and you break it into two pieces, both pieces can be positively charged.
接下来就精彩了。第三个方程是法拉第定律，它描述了变化的磁场如何产生电场。你可以看到，这个方程构成了我之前提到的发电机的理论基础。最后一个方程是安培定律，麦克斯韦对其进行了重要的修正。安培最初的定律表明电流会产生磁场。但麦克斯韦在此基础上进行了改进，指出变化的电场也会产生磁场。
Then things get really interesting. The third equation is Faraday’s law, which describes how changing magnetic fields produce electric fields. You can see how this equation serves as the theoretical foundation of the electric generators I talked about earlier. The last equation is Ampère’s law, which Maxwell modified in important ways. Ampère’s original law showed that an electric current generated a magnetic field. But by the time he was done with it, Maxwell had added a refinement, that a changing electric field creates a magnetic field.
通过对这四个方程进行推导，麦克斯韦预言了电磁波在真空中传播的存在。不仅如此，他甚至还能计算出这些波的传播速度。真正令人震惊的结果是，它们的速度与光速相同。换句话说，他得出结论：光本身也是一种电磁波！
By playing around with the four equations, Maxwell predicted the existence of electromagnetic waves traveling through empty space. What’s more, he could even calculate the speed of these waves. The truly shocking result was that their speed was the same as the speed of light. In other words, he concluded, light itself had to be an electromagnetic wave!
安培、法拉第和麦克斯韦这几位科学家深知，他们正站在一场彻底革命的边缘。一个世纪以来，研究人员一直在努力认真地研究电，而现在，这几位科学家却不断取得突破性的进展。我有时不禁好奇，他们晚上是怎么睡得着的。
These scientists—Ampère, Faraday, and Maxwell—knew they were on the brink of a total revolution. Researchers had been trying to understand electricity in a serious way for a century, but now these guys were constantly breaking new ground. I sometimes wonder how they managed to sleep at night.
麦克斯韦方程组因其在1861年所整合的理论体系，堪称十九世纪物理学的巅峰之作，尤其对于牛顿和爱因斯坦之间的所有物理学而言更是如此。如同所有意义深远的发现一样，它们也为日后统一基础科学理论的努力指明了方向。
Maxwell’s equations, because of what they brought together in 1861, were really the crowning achievement of nineteenth-century physics, most certainly for all physics between Newton and Einstein. And like all profound discoveries, they pointed the way for further efforts to try to unify fundamental scientific theories.
自麦克斯韦以来，物理学家们投入了无数精力，试图建立一个统一的理论来解释自然界的四种基本力：电磁力、强核力、弱核力和引力。阿尔伯特·爱因斯坦在生命的最后三十年里，致力于将电磁力和引力结合起来，最终建立了统一场论，但最终以失败告终。
Ever since Maxwell, physicists have spent incalculable efforts trying to develop a single unified theory of nature’s four fundamental forces: the electromagnetic, strong nuclear, weak nuclear, and gravitational forces. Albert Einstein spent the last thirty years of his life in a failed effort to combine electromagnetism and gravity in what became known as a unified field theory.
对统一的探索仍在继续。阿卜杜勒·萨拉姆、谢尔顿·格拉肖和史蒂文·温伯格因将电磁力和弱核力统一为所谓的电弱力而荣获1979年诺贝尔物理学奖。许多物理学家正试图将电弱力和强核力统一为所谓的大统一理论（简称GUT）。实现这种程度的统一将是一项惊人的成就，堪比麦克斯韦的理论。如果有一天，某位物理学家能够将引力与大统一理论结合起来，创造出许多人所说的万物理论——那将是物理学中最神圣的圣杯。统一是一个伟大的梦想。
The search for unification goes on. Abdus Salam, Sheldon Glashow, and Steven Weinberg won the Nobel Prize in 1979 for unifying electromagnetism and the weak nuclear force into what’s known as the electro-weak force. Many physicists are trying to unify the electroweak force and the strong nuclear force into what is called a grand unified theory, or GUT, for short. Achieving that level of unification would be a staggering accomplishment, on a par with Maxwell’s. And if, somehow, somewhere, a physicist ever manages to combine gravity with GUT to create what many call a theory of everything—well, that will be the holiest of Holy Grails in physics. Unification is a powerful dream.
这就是为什么在我的电磁学课程中，当我们最终完整地领略到麦克斯韦方程组的精髓和简洁之美时，我会把它们投影到整个讲堂，并向学生们分发鲜花，共同庆祝这一重要的里程碑。如果你能接受一点悬念，你可以在第15章中读到更多相关内容。
That’s why, in my Electricity and Magnetism course, when we finally see all of Maxwell’s equations in their full glory and simplicity, I project them all around in the lecture hall and I celebrate this important milestone with the students by handing out flowers. If you can handle a little suspense, you will read more about this in chapter 15.
第九章
CHAPTER 9
节能——再加上改变……
Energy Conservation—Plus ça change…
多年来，我最受欢迎的演示之一就是冒着生命危险，把头直接放在一个小型拆迁球的路径上——必须说明的是，这只是个迷你版的拆迁球，但我向你们保证，它足以致命。拆迁队使用的拆迁球可能由一个重约一千公斤的球形配重组成，而我的拆迁球则由一个15公斤重的球形配重（约33磅）制成。我站在讲堂的一侧，背靠着墙，双手紧紧握住球形配重，直到下巴。松开球形配重时，我必须格外小心，不能用力推它，哪怕是一点点也不行。任何一点推力都肯定会伤到我——或者，正如我所说，甚至可能要了我的命。我要求我的学生们不要打扰我，不要发出任何声音，甚至可以屏住呼吸一会儿——否则，我说，这可能是我的最后一堂课了。
One of the most popular demonstrations I’ve done through the years involves risking my life by putting my head directly in the path of a wrecking ball—a mini version of a wrecking ball, it must be said, but one that could easily kill me, I assure you. Whereas the wrecking balls used by demolition crews might be made from a bob, or spherical weight, of about a thousand kilos, I construct mine with a 15-kilo bob—about 33 pounds. Standing at one side of the lecture hall, with my head backed up against the wall, I hold the bob in my hands, snug up to my chin. When releasing it I must be extremely careful not to give it any kind of a push, not even a tiny little bit of a shove. Any push at all and it will surely injure me—or, as I say, possibly even kill me. I ask my students not to distract me, to make no noise, and even to stop breathing for a while—if not, I say, this could be my last lecture.
我必须承认，每次做这个演示时，当球回荡过来时，我都会感到肾上腺素飙升；尽管我确信物理定律会保护我，但站在那里看着它飞到离我的下巴只有一丝距离的地方，仍然会让我感到紧张。本能地，我我咬紧牙关。事实上，我总是会闭上眼睛！你可能会问，是什么驱使我做这个演示？我对物理学中最重要的概念之一——能量守恒定律——充满信心。
I have to confess that every time I perform this demonstration, I feel an adrenaline rush as the ball comes swinging back my way; as sure as I am that the physics will save me, it is always unnerving to stand there while it comes flying up to within a whisker of my chin. Instinctively I clench my teeth. And the truth is, I always close my eyes too! What, you may ask, what possesses me to perform this demonstration? My utter confidence in one of the most important concepts in all of physics—the law of the conservation of energy.
我们世界最奇妙的特征之一，就是一种能量形式可以转化为另一种形式，然后再转化为另一种，如此往复，甚至可以转化回原来的形式。能量可以转化，但永远不会消失，也不会消失。事实上，这种转化无时无刻不在发生。所有文明，不仅是我们自己的文明，甚至包括技术最落后的文明，都依赖于这一过程，只是形式各异。最显而易见的例子就是食物对我们的作用：将食物中的化学能（主要以碳的形式储存）转化为一种叫做三磷酸腺苷（ATP）的化合物，ATP储存着我们细胞进行各种活动所需的能量。当我们点燃篝火时，也是同样的道理：将木材或木炭中储存的化学能（它们中的碳与氧结合）转化为热量和二氧化碳。
One of the most remarkable features of our world is that one form of energy can be converted into another form, and then into another and another, and even converted back to the original. Energy can be transformed but never lost, and never gained. In fact, this transformation happens all the time. All civilizations, not only ours but even the least technologically sophisticated, depend on this process, in many variations. This is, most obviously, what eating does for us; converting the chemical energy of food, mostly stored in carbon, into a compound called adenosine triphosphate (ATP), which stores the energy our cells can use to do different kinds of work. It’s what happens when we light a campfire, converting the chemical energy stored in wood or charcoal (the carbon in each combines with oxygen) into heat and carbon dioxide.
正是能量驱动着箭矢从弓上射出，将拉弓时积累的势能转化为动能，从而推动箭矢向前飞行。在枪械中，能量则是将火药的化学能转化为快速膨胀气体的动能，推动子弹射出枪膛。骑自行车时，驱动脚踏板的能量最初来源于你早餐或午餐的化学能，你的身体将其转化为另一种形式的化学能（ATP）。你的肌肉利用这种化学能，将其一部分转化为机械能，从而收缩和放松肌肉，使你能够踩动脚踏板。汽车电池中储存的化学能会在你转动点火钥匙时转化为电能。一部分电能进入气缸，点燃汽油混合物，释放汽油燃烧产生的化学能。这种能量随后转化为热量，增加气缸内气体的压力，进而推动活塞运动。活塞带动曲轴旋转，最终驱动发动机运转。变速器将能量传递到车轮，使车轮转动。通过这一奇妙的过程，汽油的化学能得以利用，使我们能够驾驶车辆。
It’s what drives an arrow through the air once it’s been shot from a bow, converting the potential energy, built up when you pull the bowstring back into kinetic energy, propelling the arrow forward. In a gun, it’s the conversion of chemical energy from the gunpowder into the kinetic energy of rapidly expanding gas that propels bullets out of the barrel. When you ride a bicycle, the energy that pushes the pedals began as the chemical energy of your breakfast or lunch, which your body converted into a different form of chemical energy (ATP). Your muscles then use that chemical energy, converting some of it into mechanical energy, in order to contract and release your muscles, enabling you to push the pedals. The chemical energy stored in your car battery is converted to electric energy when you turn the ignition key. Some electric energy goes to the cylinders, where it ignites the gasoline mixture, releasing the chemical energy released by the gasoline as it burns. That energy is then converted into heat, which increases the pressure of the gas in the cylinder, which in turn pushes the pistons. These turn the crankshaft, and the transmission sends the energy to the wheels, making them turn. Through this remarkable process the chemical energy of the gasoline is harnessed to allow us to drive.
混合动力汽车的部分原理正是反向运用了这一过程。它们将汽车的部分动能（例如踩刹车时产生的动能）转化为电能，储存在电池中，并驱动电动机运转。在燃油炉中，油的化学能转化为热能，加热系统中的水温升高，然后由水泵将热水输送到散热器。在霓虹灯中，流经氖气管的电荷的动能转化为可见光。
Hybrid cars rely in part on this process in reverse. They convert some of the kinetic energy of a car—when you step on the brakes—into electric energy that is stored in a battery and can run an electric motor. In an oil-fired furnace, the chemical energy of the oil is converted into heat, which raises the temperature of water in the heating system, which a pump then forces through radiators. In neon lights, the kinetic energy of electric charges moving through a neon gas tube is converted into visible light.
这些应用似乎无穷无尽。在核反应堆中，储存在铀或钚原子核中的核能转化为热能，热能使水变成蒸汽，蒸汽驱动涡轮机发电。储存在化石燃料（不仅包括石油和汽油，还包括煤炭和天然气）中的化学能转化为热能，在发电厂中，最终转化为电能。
The applications are seemingly limitless. In nuclear reactors, the nuclear energy that is stored in uranium or plutonium nuclei is converted into heat, which turns water into steam, which turns turbines, which create electricity. Chemical energy stored in fossil fuels—not only oil and gasoline but also coal and natural gas—is converted into heat, and, in the case of a power plant, is ultimately converted to electrical energy.
制作一个电池，就能轻松见证能量转换的奇妙。电池种类繁多，从传统汽车或混合动力汽车的电池，到无线鼠标和手机的电池，不一而足。信不信由你，你只需一个土豆、一枚硬币、一根镀锌钉和两段铜线（每段约 15 厘米长，两端各刮去半英寸的绝缘层），就能制作一个简易电池。将钉子一端插入土豆的大部分，另一端切开一个小口，放入硬币。将其中一段铜线的一端固定在钉子上（或缠绕在钉头上）；将另一段铜线的一端固定在硬币上，或将其滑入小口，使其与硬币接触。然后，将两段铜线的自由端分别接触圣诞树彩灯的引线。彩灯应该会闪烁一下。恭喜！你可以在 YouTube 上找到许多类似的装置——何不自己动手试试呢？
You can witness the wonders of energy conversion easily by making a battery. There are lots of different kinds of batteries, from those in your conventional or hybrid car to those powering your wireless computer mouse and cell phone. Believe it or not, but you can make a battery from a potato, a penny, a galvanized nail, and two pieces of copper wire (each about 6 inches long, with a half-inch of insulation scraped off at each end). Put the nail most of the way into the potato at one end, cut a slit at the other end for the penny, and put the penny into the slit. Hold the end of one piece of wire on the nail (or wrap it around the nail head); hold the other piece of wire on the penny or slide it into the slit so it touches the penny. Then touch the free ends of the wires to the little leads of a Christmas tree light. It should flicker a little bit. Congratulations! You can see dozens of these contraptions on YouTube—why not give it a try?
显然，我们周围无时无刻不在发生能量转换。但有些能量比其他能量更显而易见。其中最违反直觉的一种就是我们所说的重力势能。虽然我们通常不会认为静止的物体具有能量，但它们确实有能量；在某些情况下，它们的能量还相当大。由于重力总是试图将物体拉向地心，因此从一定高度落下的物体都会获得速度。在这个过程中，物体会损失重力势能，但会获得动能——能量既没有损失也没有产生；这是一个零和博弈！如果一个质量为m的物体沿垂直距离h下落，它的势能会减少mgh（g是重力加速度，约为 9.8 米/秒²），但它的动能会增加相同的量。如果你将物体向上移动垂直距离h，它的重力势能会增加mgh，而你必须产生这部分能量（你必须做功）。
Clearly, conversions of energy are going on around us all of the time, but some of them are more obvious than others. One of the most counterintuitive types is that of what we call gravitational potential energy. Though we don’t generally think of static objects as having energy, they do; in some cases quite a bit of it. Because gravity is always trying to pull objects down toward the center of the Earth, every object that you drop from a certain height will pick up speed. In doing so, it will lose gravitational potential energy but it will gain kinetic energy—no energy was lost and none was created; it’s a zero sum game! If an object of mass m falls down over a vertical distance h, its potential energy decreases by an amount mgh (g is the gravitational acceleration, which is about 9.8 meters per second per second), but its kinetic energy will increase by the same amount. If you move the object upward over a vertical distance h, its gravitational potential energy will increase by an amount mgh, and you will have to produce that energy (you will have to do work).
如果一本质量为 1 千克（2.2 磅）的书放在离地面 2 米（约 6.5 英尺）高的架子上，那么当它落到地面时，它的重力势能将减少 1 × 9.8 × 2 = 19.6 焦耳，但当它撞击地面时，它的动能仍为 19.6 焦耳。
If a book with a mass of 1 kilogram (2.2 pounds) is on a shelf 2 meters (about 6.5 feet) above the floor, then, when it falls to the floor, its gravitational potential energy will decrease by 1 × 9.8 × 2 = 19.6 joules but its kinetic energy will be 19.6 joules when it hits the floor.
我认为“重力势能”这个名称非常贴切。不妨这样想：如果我把书从地上拿起来放到书架上，需要消耗我19.6焦耳的能量。这部分能量就消失了吗？并没有！现在书离地面2米高，它就具有将这部分能量以动能的形式“返还”给我的“潜力”——无论我何时把它扔到地上，无论是第二天还是明年！书离地面越高，它所拥有的“潜在”能量就越多，当然，这部分额外的能量需要我付出。
I think the name gravitational potential energy is an excellent name. Think of it this way. If I pick the book up from the floor and place it on the shelf, it takes 19.6 joules of my energy to do so. Is this energy lost? No! Now that the book is 2 meters above the floor, it has the “potential” of returning that energy back to me in the form of kinetic energy—whenever I drop it on the floor, be it the next day or the next year! The higher the book is above the floor, the more energy is “potentially” available, but, of course I have to provide that extra energy to place the book higher.
类似地，拉弓射箭需要能量。这种能量储存在弓中，在你选择时机，它可以“潜在地”转化为动能，从而赋予箭矢速度。
In a similar way, it takes energy to pull the string of a bow back when you want to shoot an arrow. That energy is stored in the bow and it is “potentially” available, at a time of your chosing, to convert that potential energy into kinetic energy, which gives the arrow its speed.
现在，我可以用一个简单的等式来向你展示一些东西。真是妙极了。如果你愿意花点时间了解一下数学，你就会明白伽利略最著名的（非）实验为什么有效。据说他从比萨斜塔上扔下质量（也就是重量）不同的球，以证明球的下落速度与质量无关。根据牛顿运动定律，运动物体的动能（KE）与其质量和速度的平方成正比；其公式为KE = 1/2 mv²。由于我们知道物体的重力势能变化会转化为动能，因此我们可以说mgh等于 1/2 mv²，所以公式为mgh = 1/2 mv² 。如果等式两边同时除以m ，m就完全消失了，所以公式为gh = 1/2 v² 。然后为了去掉分数，我们将等式两边乘以 2，得到 2gh = v2 。这意味着速度v （伽利略测试的就是速度）等于2gh的平方根。*请注意，质量在等式中完全消失了！它根本就不是一个因素——速度与质量无关。举个具体的例子，如果我们从100米的高度扔下一块石头（任何质量），在忽略空气阻力的情况下，它将以大约45米/秒的速度落到地面，也就是大约100英里/小时。
Now, there is a simple equation I can use to show you something quite wonderful. If you bear with me for just a bit of math, you’ll see why Galileo’s most famous (non)experiment works. Recall that he was said to have dropped balls of different mass (thus different weight) from the Leaning Tower of Pisa to show that their rate of falling was independent of their mass. It follows from Newton’s laws of motion that the kinetic energy (KE) of a moving object is proportional both to the mass of the object and to the square of its speed; the equation for that is KE = 1/2 mv2. And since we know that the change in gravitational potential energy of the object is converted to kinetic energy, then we can say that mgh equals 1/2 mv2, so you have the equation mgh = 1/2mv2. If you divide both sides by m, m disappears from the equation entirely, and you have gh = 1/2v2. Then to get rid of the fraction we multiply both sides of the equation by 2, to get 2gh = v2. This means that v, the speed, which is what Galileo was testing for, equals the square root of 2gh.* And note that mass has completely disappeared from the equation! It is literally not a factor—the speed does not depend on the mass. To take a specific example, if we drop a rock (of any mass) from a height of 100 meters, in the absence of air drag it will hit the ground with a speed of about 45 meters per second, or about 100 miles per hour.
想象一下，一块岩石（质量不限）从几十万英里之外落到地球上。它进入地球大气层时的速度是多少？很遗憾，我们不能简单地用上面提到的速度是√2gh的公式来计算，因为引力加速度与到地球的距离密切相关。在月球附近（大约24万英里），地球的引力加速度比地球表面附近小约3600倍。我就不赘述计算过程了，相信我，它的速度大约是每小时25000英里！
Imagine a rock (of any mass) falling from a few hundred thousand miles away to the Earth. With what speed would it enter the Earth’s atmosphere? Unfortunately, we cannot use the above simple equation that the speed is the square root of 2gh because the gravitational acceleration depends strongly on the distance to Earth. At the distance of the Moon (about 240,000 miles), the gravitational acceleration due to Earth is about 3,600 times smaller than what it is close to the surface of the Earth. Without showing you the math, take my word for it, the speed would be about 25,000 miles per hour!
或许你现在能理解引力势能对天文学的重要性了。正如我将在第13章讨论的那样，当物质一块从遥远的地方落到中子星上，它以大约每秒 10 万英里的速度撞击中子星，没错，是每秒！如果这块岩石的质量只有 1 千克，那么它的动能将约为 13 万亿焦耳（13 × 10¹⁵ 焦耳），这大约相当于一座大型（1000 兆瓦）发电厂半年左右产生的能量。
Perhaps you can now understand how important gravitational potential energy is in astronomy. As I will discuss in chapter 13, when matter falls from a large distance onto a neutron star, it crashes onto the neutron star with a speed of roughly 100,000 miles per second, yes, per second! If the rock had a mass of only 1 kilogram, its kinetic energy would then be about 13 thousand trillion (13 × 1015) joules, which is roughly the amount of energy that a large (1,000 MW) power plant produces in about half a year.
不同类型的能量可以相互转化，然后再转化回来，这本身就足够令人惊叹了，但更令人惊叹的是，能量永远不会有任何净损失。永远不会。太神奇了。这就是为什么拆迁球从来没能要了我的命。
The fact that different types of energy can be converted into one another and then back again is remarkable enough, but what is even more spectacular is that there is never any net loss of energy. Never. Amazing. This is why the wrecking ball has never killed me.
当我把一个15公斤重的球拉到下巴处，垂直距离为h时，球的重力势能增加了mgh。当我松开球时，球在重力的作用下开始摆动，mgh转化为动能。这里，h是我下巴到绳子末端摆锤最低点的垂直距离。当球摆动到最低点时，它的动能为mgh。当球完成摆动弧线到达最高点时，动能又转化为势能——这就是为什么钟摆在最高点时，球会短暂地停止运动。如果没有动能，就不会有运动。但这只是短暂的一瞬，因为球随后会再次下落，开始反向摆动，势能再次转化为动能。动能和势能之和称为机械能，在没有摩擦力（本例中是空气对摆锤的阻力）的情况下，总机械能不会改变——它是守恒的。
When I pull the 15 kilogram ball up to my chin over a vertical distance h, I increase its gravitational potential energy by mgh. When I drop the ball, it begins to swing across the room due to the force of gravity, and mgh is converted into kinetic energy. Here, h is the vertical distance between my chin and the lowest position of the bob at the end of the string. As the ball reaches its lowest point in the swing, its kinetic energy will be mgh. As the ball completes its arc and reaches the upper limit of its swing, that kinetic energy is converted back into potential energy—which is why, at the very height of a pendulum swing, the ball stops for a moment. If there’s no kinetic energy, there’s no movement. But that is for just the slightest moment, because then the ball goes back down again, on its reverse swing, and potential energy is converted again into kinetic energy. The sum of kinetic energy and potential energy is called mechanical energy, and in the absence of friction (in this case air drag on the bob), the total mechanical energy does not change—it is conserved.
这意味着，只要不给小球施加任何额外的能量，它最高只能落到释放点的位置。空气阻力是我的安全保障。摆锤的机械能只有极小一部分会被空气阻力带走并转化为热能。因此，摆锤最终停在离我下巴只有八分之一英寸的地方，正如你在8.01课程第11讲的视频中看到的那样。苏珊看过我演示三次——每次她都吓得发抖。有人曾经问我是否经常练习，我总是回答说：回答我真实的问题：我不需要练习，因为我百分之百相信能量守恒定律。
This means that the ball can go no higher than the exact spot from which it was released—as long as no extra energy is imparted to it anywhere along the way. Air drag is my safety cushion. A very small amount of the mechanical energy of the pendulum is sucked away by air drag and converted into heat. As a result, the bob stops just one-eighth of an inch from my chin, as you can see in the video of lecture 11 from course 8.01. Susan has seen me do the demonstration three times—she shivers each time. Someone once asked me if I practiced a lot, and I always answer with what is true: that I do not have to practice as I trust the conservation of energy, 100 percent.
但是，如果我在松手时稍微用力推一下球——比如说我刚才咳嗽了一下，导致球稍微弹了一下——它就会摆动到比我松手时略高的位置，然后猛地撞到我的下巴。
But if I were to give the ball the slightest little push when I let it go—say I had coughed just then and that caused me to give the ball some thrust—it would swing back to a spot a little higher than where I released it from, smashing into my chin.
能量守恒定律的发现主要归功于十九世纪中期英国酿酒商之子詹姆斯·焦耳的工作。他的工作对理解能量的本质至关重要，以至于能量的国际计量单位——焦耳——就是以他的名字命名的。他的父亲曾送他和他的兄弟去跟随著名的实验科学家约翰·道尔顿学习。显然，道尔顿对焦耳的教导卓有成效。焦耳继承了父亲的酿酒厂后，在酿酒厂的地下室里进行了一系列创新性的实验，以巧妙的方式探索电、热和机械能的特性。他的一项发现是，电流会在导体中产生热量。他通过将不同种类金属的线圈通电后放入装有水的容器中，并测量其温度变化，发现了这一现象。
The conservation of energy was discovered largely due to the work of a mid-nineteenth-century English brewer’s son, James Joule. So important was his work to understanding the nature of energy that the international unit by which energy is measured, the joule, was named after him. His father had sent him and his brother to study with the famous experimental scientist John Dalton. Clearly Dalton taught Joule well. After Joule inherited his father’s brewery, he performed a host of innovative experiments in the brewery’s basement, probing in ingenious ways into the characteristics of electricity, heat, and mechanical energy. One of his discoveries was that electric current produces heat in a conductor, which he found by putting coils of different kinds of metal with current running through them into jars of water and measuring their changes in temperature.
焦耳的根本洞见在于他发现热是一种能量形式，这推翻了多年来人们普遍接受的热的认知。人们曾认为热是一种流体，称为热质（caloric），我们现代英语单词卡路里（calorie）即源于此。当时的普遍观点认为，这种流体热会从高浓度区域流向低浓度区域，并且热质既不能被创造也不能被消灭。然而，焦耳注意到，热的产生方式多种多样，这表明热的本质并非如此。例如，他研究了瀑布，发现瀑布底部的水温高于顶部，由此得出结论：瀑布顶部和底部之间的重力势能差转化为了热能。他还观察到，当桨轮搅动水时——这是焦耳进行的一项非常著名的实验——水温会升高。1881年，他提出了一个非常精确的公式。将桨轮动能转化为热能的结果。
Joule had the fundamental insight that heat is a form of energy, which refuted what had been the widely accepted understanding of heat for many years. Heat, it was thought, was a kind of fluid, which was called caloric—from which our contemporary word calorie derives—and the belief at the time was that this fluid heat flowed from areas of high concentration to low, and that caloric could never be either created or destroyed. Joule made note, though, that heat was produced in many ways that suggested it was of a different nature. For example, he studied waterfalls and determined that the water at the bottom was warmer than that at the top, and he concluded that the gravitational potential energy difference between the top and bottom of the waterfall was converted into heat. He also observed that when a paddle wheel was stirring water—a very famous experiment that Joule performed—it raised the temperature of the water, and in 1881 he came up with remarkably accurate results for the conversion of the kinetic energy of the paddle wheel into heat.
在这个实验中，焦耳将一组桨叶连接到一个装有水的容器中，并通过滑轮和一根绳子固定，绳子上悬挂着一个重物。随着重物下落，绳子带动桨叶的轴转动，从而使桨叶在水容器中旋转。更准确地说，他用绳子将一个质量为m 的物体下落了一段距离h。势能的变化为mgh，该装置将势能转化为桨叶的旋转（动）能，进而加热了水。下图是该装置的示意图：
In this experiment Joule connected a set of paddles in a container of water to a pulley and a string from which he suspended a weight. As the weight lowered, the string turned the shaft of the paddles, rotating them in the water container. More technically, he lowered a mass, m, on a string over a distance, h. The change in potential energy was mgh, which the contraption converted into the rotational (kinetic) energy of the paddle, which then heated the water. Here is an illustration of the device:
这项实验的精妙之处在于，焦耳能够精确计算出他传递给水的能量——等于mgh。由于水阻碍了桨叶的快速旋转，重物缓慢下落。因此，重物落地时的动能可以忽略不计。这样，所有可用的重力势能都传递给了水。
What made the experiment so brilliant is that Joule was able to calculate the exact amount of energy he was transferring to the water—which equaled mgh. The weight came down slowly, because the water prevented the paddle from rotating fast. Therefore the weight hit the ground with a negligible amount of kinetic energy. Thus all the available gravitational potential energy was transferred to the water.
焦耳是多少？简单来说，如果你将一个1千克的物体从0.1米（10厘米）的高度自由落体，该物体的动能增加了mgh，大约是1焦耳。这听起来似乎不多，但焦耳的能量累积起来相当可观。美国职业棒球大联盟的投手要想以接近100英里/小时的速度投出棒球，大约需要140焦耳的能量。能量，大约相当于将一蒲式耳（140 个 100 克重的苹果）提升 1 米所需的能量。*
How much is a joule? Well, if you drop a 1-kilogram object 0.1 meters (10 centimeters), the kinetic energy of that object has increased by mgh, which is about 1 joule. That may not sound like much, but joules can add up quite quickly. In order to throw a baseball just under 100 miles per hour, a Major League Baseball pitcher requires about 140 joules of energy, which is about the same amount of energy required to lift a bushel of 140 hundred-gram apples 1 full meter.*
一百四十焦耳的动能如果以极快的速度、高度集中的方式释放，足以致命。如果能量分散在一两个小时内，你甚至感觉不到。如果所有这些焦耳的能量都集中在一个枕头上，猛烈地撞击你，也不会致命。但如果这些能量集中在一颗子弹、一块石头或一个棒球上，在极短的时间内集中击中你呢？情况就完全不同了。
One hundred forty joules of kinetic energy hitting you could be enough to kill you, as long as that energy is released quickly, and in a concentrated fashion. If it were spread out over an hour or two, you wouldn’t even notice it. And if all those joules were released in a pillow hitting you hard, it wouldn’t kill you. But concentrated in a bullet, say, or a rock or a baseball, in a tiny fraction of a second? A very different story.
这就引出了我们之前提到的铁球。假设你有一个1000公斤（1吨）重的铁球，从5米高的垂直高度落下。它会将大约50000焦耳的势能（mgh = 1000 × 10 × 5）转化为动能。这威力相当惊人，尤其是在短时间内释放的情况下。利用动能公式，我们也可以计算出速度。在摆动到最低点时，铁球的速度将达到每秒10米（约每小时22英里），对于一个1吨重的铁球来说，这已经是一个相当高的速度了。要亲眼目睹这种能量的威力，您可以在网上观看一段精彩的视频，视频中一个拆迁球击中了一辆误入曼哈顿建筑区的厢式货车，将货车像玩具车一样撞倒在地：www.lionsdenu.com/wrecking-ball-vs-dodge-mini-van/。
Which brings us back to wrecking balls. Suppose you had 1,000-kilogram (1-ton) wrecking ball, which you drop over a vertical distance of 5 meters. It will convert about 50,000 joules of potential energy (mgh = 1,000 × 10 × 5) into kinetic energy. That’s quite a wallop, especially if it’s released in a very short time. Using the equation for kinetic energy, we can solve for speed too. At the bottom of its swing the ball would be moving at a speed of 10 meters per second (about 22 miles per hour), which is a pretty high speed for a 1-ton ball. To see this kind of energy in action, you can check out an amazing video online of a wrecking ball hitting a minivan that had strayed into a Manhattan construction zone, knocking the van over as though it were a toy car: www.lionsdenu.com/wrecking-ball-vs-dodge-mini-van/.
我们需要多少食物能量？
How Much Food Energy Do We Need?
我们可以通过思考生命最基本过程中涉及的焦耳数，来体会维持我们文明运转的能量转换的惊人壮举。例如，人体一天会产生大约1000万焦耳的体热。除非发烧，否则人体的正常体温约为华氏98.6度（摄氏37度），并以红外辐射的形式平均每天散发约100焦耳的热量。每秒辐射的能量；粗略估计每天大约1000万焦耳。然而，这取决于气温和人体的体型。体型越大，每秒辐射的能量就越多。你可以将其与灯泡辐射的能量进行比较；1瓦相当于每秒消耗1焦耳的能量，因此每秒100焦耳等于100瓦，这意味着平均而言，人体辐射的能量与100瓦的灯泡大致相同。你不会像灯泡那样感到热，因为你的热量分布在更大的区域。当你想到电热毯只能产生50瓦的功率时，你现在应该明白为什么（我相信你也知道），在冬天，床上有人陪伴比电热毯舒适得多。
We can come to appreciate the amazing feats of conversion of energy that keep our civilization running by considering the amount of joules involved in the most basic of our life processes. Consider, for example, that in one day a human body generates about 10 million joules of body heat. Unless you’re running a fever, your body runs roughly at a temperature of 98.6 degrees Fahrenheit (37 degrees Celsius), and radiates heat in the form of infrared radiation at the rate, on average, of about 100 joules per second; very roughly about 10 million joules per day. However, this does depend on air temperature and the size of the human being. The larger the person, the more energy s/he radiates per second. You can compare that to the energy radiated by a lightbulb; 1 watt is equivalent to the expenditure of 1 joule per second, so 100 joules per second equals 100 watts, which means that on average, people radiate at roughly the same level as a 100-watt lightbulb. You don’t feel as hot as a lightbulb because your heat is distributed over a much larger area. When you think that an electric blanket only produces 50 watts, you now understand why, as I’m sure you already know, in winter it’s much nicer to have a human being with you in bed than an electric blanket.
能量的单位有很多种：空调用英热单位（BTU）；电能用千瓦时；原子物理学用电子伏特；天文学家用尔格。1英热单位约等于1055焦耳；1千瓦时相当于3.6 × 10⁶焦耳；1电子伏特等于1.6 × 10⁻¹⁹焦耳；1尔格等于10⁻⁷焦耳。我们都熟悉的一个非常重要的能量单位是卡路里。1卡路里约等于4.2焦耳。因此，我们身体每天大约产生1000万焦耳的能量，而我们消耗的卡路里却略高于200万卡路里。但这怎么可能呢？我们每天应该只摄入大约2000卡路里。当你在食品包装上看到“卡路里”这个词时，标签上的真正含义是“千卡”（kilocalorie），也就是一千卡路里，有时会用大写字母“C”来表示。这样做是为了方便，因为一卡路里是一个非常小的单位：它指的是将1克水的温度升高1摄氏度所需的能量。所以，为了每天吸收1000万焦耳的能量，你每天大约需要摄入2400千卡（或卡路里）的食物。如果你摄入的热量远远超过这个量，那么迟早你会付出代价。正如我们很多人知道却试图忽略的那样，这其中的道理相当残酷。
There are dozens of different units for energy: BTUs for air conditioners; kilowatt-hours for electricity; electron volts for atomic physics; ergs for astronomers. A BTU is about 1,055 joules; a kilowatt-hour is the equivalent of 3.6 × 106 joules; an electron volt is 1.6 × 10–19 joules; 1 erg is 10–7 joules. One very important unit of energy we are all familiar with is the calorie. A calorie is close to 4.2 joules. So, as our bodies generate roughly 10 million joules every day, we are expending a little over 2 million calories. But how can that be? We’re supposed to eat only about 2,000 calories a day. Well, when you read calorie on food packages, what the label writers really mean is kilocalorie, a thousand calories, sometimes indicated by spelling the word calorie with a capital C. This is done for convenience, because a single calorie is a very small unit: the amount of energy required to raise the temperature of 1 gram of water 1 degree Celsius. So, in order to radiate 10 million joules per day, you have to eat roughly 2,400 kilocalories (or Calories) of food a day. And if you eat a lot more than that, well, you pay a price sooner or later. The math here is pretty unforgiving, as too many of us know but try to ignore.
那么我们一天中所有的体力活动呢？难道我们不需要吃东西来补充能量吗？比如说上下楼梯、在家忙碌、或者使用吸尘器？家务活很累人，所以我们肯定消耗了很多能量，对吧？嗯，我恐怕我要告诉你一个令人失望的消息。你我一天所做的事情消耗的能量少得可怜，如果你想通过运动来平衡饮食，完全可以忽略运动，除非你去健身房进行高强度锻炼。
What about all of the physical activity we do in a day? Don’t we also have to eat to fuel that? Going up and down stairs, say, or puttering around the house, or running the vacuum cleaner? Housework can be exhausting, so we must be expending a lot of energy, right? Well, I’m afraid I have a surprise for you. It’s really very disappointing. The kind of activity that you and I do in one day uses so embarrassingly little energy that you can completely neglect it if you expect to balance out food intake, unless you go to the gym for a really hard workout.
假设你选择走楼梯而不是乘电梯上三层楼去办公室。我知道很多人觉得走楼梯很环保，但请算算这笔账。假设这三层楼的高度约为 10 米，你每天走三趟。因为我不了解你，所以我们假设你的体重约为 70 公斤（154 磅）。走三趟楼梯需要多少能量？我们再假设一下，一天走五趟呢？假设你真的非常环保。每天五次，每次都走三层楼。你需要产生的能量是mgh，其中h是第一层和第四层之间的高度差。我们将 70 公斤 ( m ) 乘以 10 米每秒 ( g ) 的重力加速度 (g ) 乘以 10 米 ( h ) 再乘以 5（因为你每天走五趟），结果如下：35,000 焦耳。想想你身体每天辐射的1000万焦耳吧。你以为为了这区区35000焦耳就得多吃点吗？别想了。这点热量根本不算什么，只占总热量的0.35%。但这并不能阻止商家对燃脂器材做出荒谬的宣传。我今天早上翻阅了一份高端电子产品邮购目录，发现一则“可穿戴负重”的广告，声称可以“在日常活动中额外燃烧卡路里”。你或许会喜欢手臂和腿感觉更重的感觉（虽然我也不知道为什么），而且穿戴它们确实能锻炼肌肉，但别指望靠这种“折磨”就能减掉多少体重！
Suppose you take the stairs to climb three floors to your office instead of taking the elevator. I know plenty of people who feel virtuous for taking the stairs, but do the math. Say those three floors cover a height of about 10 meters, and you walk up them three times per day. Since I don’t know you, let’s give you a mass of about 70 kilograms—154 pounds. How much energy does it take to walk up those stairs three times? Let’s be really virtuous—how about five times a day? Let’s assume you really go out of your way. Five times a day, three floors up. The energy you would have to produce is mgh, where h is the difference in height between the first and the fourth floor. We multiply the 70 kilograms (m) by 10 meters per second per second (g) by 10 meters (h) by 5, since you do it five times a day, and here’s what we get: 35,000 joules. Compare that to the 10 million joules per day that your body radiates. You think you have to eat a little bit more for these lousy 35,000 joules? Forget it. It’s nothing: just one-third of 1 percent of the total. But that doesn’t stop marketers from making absurd claims about calorie-burning equipment. I just opened a mail-order catalog this morning that features high-end gadgets and found an ad for “wearable weights” that provide “extra calorie burning during normal daily activity.” You might enjoy the feeling of your arms and legs being heavier (though I’m not sure why), and wearing them will build up muscle, but don’t expect to lose significant weight by this kind of punishment!
聪明的读者会注意到，我们当然不可能一天上下五次楼梯而不下楼。下楼时，那35000焦耳的能量会以热量的形式释放出来，存在于你的肌肉、鞋子和地板上。如果你跳起来，爬楼梯时积累的所有重力势能都会转化为身体的动能——你很可能会骨折一两处。所以，虽然你爬楼梯需要积累这35000焦耳的能量，但你并不会因此而失去这些能量。当你落地时，除非你能安装一个非常巧妙的装置，将你的动能转换成电能（这正是混合动力汽车所做的），否则它们就无法以可用的形式返回地面。
Now a clever reader will note that of course we cannot go up the stairs five times a day without coming down. When you come down, those 35,000 joules will be released, in the form of heat in your muscles, your shoes, and the floor. If you were to jump, all of the gravitational potential energy you built up climbing the stairs would be converted to the kinetic energy of your body—and you’d probably break a bone or two. So while you had to come up with the 35,000 joules to get there, you don’t get them back in a usable form when you come down, unless you can rig up a very clever device to take your kinetic energy and convert it to, say, electricity—which is exactly what hybrid cars do.
换个角度来看。假设你把爬楼梯的时间分散到一天中的十个小时里，比如早上爬一两次，下午爬两次，傍晚再爬一次。在这十个小时，也就是36000秒内，你大约产生了35000焦耳的能量。坦白说，这少得可怜——平均下来只有大约1瓦。相比之下，你的身体平均每秒辐射大约100焦耳的能量，也就是100瓦。所以，你可以看出，爬楼梯消耗的能量完全可以忽略不计。它对你的腰围没有任何帮助。
Look at it another way. Say you spread that stair climbing out over ten hours in a day, maybe once or twice in the morning, twice in the afternoon, and a final time in the early evening. In those ten hours, 36,000 seconds, you generated about 35,000 joules. This is, to be blunt, absurdly little—an average of about 1 watt. Compare that with your body, which radiates on average about 100 joules per second, or 100 watts. So, you can see, the energy burned by your stair climbing is completely negligible. It won’t do anything for your waistline.
然而，假设你攀登的是一座 5000 英尺高的山峰呢？为此，你需要在日常能量输出的基础上额外产生并消耗一百万焦耳的能量。而一百万焦耳与一千万焦耳相比，就不再是微不足道的了。爬完这座山后，你会感到真正的饥饿，并且确实需要更多食物。如果你用四个小时爬上这座山，那么你产生的平均功率（功率单位为焦耳/秒）相当可观，当然，平均每个小时大约是 70 瓦。因此，此时你的身体会向大脑发出一个强烈的信号：“我需要吃更多东西。”
However, suppose you climb a 5,000-foot mountain instead? To do that, you would have to generate and use a million joules on top of your regular output. And a million is no longer negligible compared to 10 million. After climbing that mountain you feel legitimately hungry, and now you really do need more food. If you walk up that mountain in four hours, the average power that you have generated (power is joules per second) is substantial, an average of 70 watts during those four hours, of course. And so now the body sends an emphatic message to your brain: “I need to eat more.”
你或许会认为，既然你消耗的能量比平时多1000万焦耳，那么你只需要比平时多吃10%（也就是多吃240卡路里）就行了，因为很明显，一百万只是一千万的十分之一。但事实并非如此，你可能凭直觉就知道这一点。你必须比平时多吃很多，因为人体将食物转化为能量的效率并不高——从物理学的角度来看。人类平均的转化率最高也只有40%——也就是说，我们最多只能将摄入的卡路里的40%转化为可用能量。其余的都以热量的形式散失了。由于能量守恒，这些热量必须散失到某个地方。因此，为了产生额外的100万焦耳能量来满足你的登山爱好，你需要额外摄入大约600卡路里，这大致相当于每天多吃一顿饭。
You might think that since you’ve used 10 percent more energy over your normal 10 million joules that you would only have to eat 10 percent more (thus 240 Calories more) than you normally eat, because it’s pretty obvious that a million is only 10 percent of 10 million. But that’s not quite true, which you probably knew intuitively. You have to eat a good bit more than normal, because the body’s food-to-energy conversion system is not particularly efficient—in physics terms. The best human beings do, on average, is 40 percent—that is, we convert at most 40 percent of our caloric intake to usable energy. The rest is lost as heat. It has to go somewhere, since energy is conserved. So to generate an extra million joules of energy to feed your mountain-climbing habit, you’ll have to eat about 600 additional Calories, the rough equivalent of an extra meal per day.
我们去哪里获取所需物品？
Where Are We Going to Get What We Need?
日常生活所需的能量之多令我震惊。假设我想洗个澡，想计算一下加热水需要多少能量。公式很简单：所需能量（以千卡为单位）等于水的质量（以千克为单位）乘以温度变化（以摄氏度为单位）。假设一个浴缸大约有100千克水（约26加仑），温度升高约50摄氏度，那么加热一个热水澡大约需要5000千卡，也就是2000万焦耳的能量。洗澡很舒服，但确实需要消耗不少能量。令人惊讶的是，在美国，能源仍然非常便宜，洗个澡只需花费大约1.5美元。两百年前，人们用柴火加热洗澡水。每千克柴火含有约1500万焦耳的能量，所以一家人洗一次澡就需要消耗掉一千克柴火的全部能量。虽然现代柴火炉的燃烧效率可达70%，但明火或200年前的炉灶将木材转化为热能的效率要低得多，而且所需时间也更长。因此，加热一个26加仑的浴缸可能需要5到10公斤的木材。难怪我们的祖先洗澡的频率远低于我们，而且一家人共用一盆洗澡水。
The amount of energy required for our everyday life activities is astonishing to me. Suppose I wanted to take a bath, and I want to calculate how much energy it takes to heat the water. The equation is very simple; the amount of energy in kilocalories required is the mass in kilograms of the water times the temperature change in Celsius. So since a bath holds about 100 kilograms of water—that’s about 26 gallons—and if we assume that the temperature increase is about 50 degrees Celsius, it takes roughly 5,000 kilocalories, or 20 million joules, of energy to produce a hot bath. Baths are lovely, but they require quite a bit of energy. The remarkable thing is that energy is still so cheap in the United States, that the bath will only cost about $1.50. Two hundred years ago, bathwater was heated with a wood fire. Firewood contains about 15 million joules per kilogram, so a family would have to get all the energy out of a kilo of wood for a single bath. While modern woodstoves can burn at 70 percent efficiency, an open fire or the stoves of 200 years ago convert wood to heat much less efficiently, and over a longer period of time, so it would probably take 5 to 10 kilos of wood to heat that 26-gallon bathtub. No wonder our ancestors bathed a lot less frequently than we do, and an entire family used the same bathwater.
以下是一些数据，可以帮助您了解家庭能源消耗情况。一台电暖器大约消耗1000瓦，这意味着一小时内，您会消耗大约360万焦耳的能量，或者用计量电能的常用单位来说，就是1千瓦时。在寒冷气候下，一台电炉大约会消耗2500瓦。窗式空调通常消耗1500瓦，而中央空调系统则会消耗大约5到20千瓦。在华氏350度（约摄氏177度）的温度下，一台电烤箱会消耗2千瓦，而一台洗碗机则会消耗大约3.5千瓦。这里有一个有趣的对比：一台配备17英寸阴极射线管显示器的台式电脑会消耗150到350瓦，而一台处于睡眠模式的电脑和显示器只会消耗20瓦或更少。低端的收音机闹钟仅消耗 4 瓦功率。由于 9 伏碱性电池总共储存约 18,000 焦耳的能量，或约 5 瓦时，因此一节电池可以为你的收音机闹钟供电一个多小时。
Here are some figures to give you a sense of household energy usage. A space heater uses roughly 1,000 watts, which means that in the course of an hour, you expend about 3.6 million joules, or, to use the common term for measuring electricity, 1 kilowatt-hour. An electric furnace in a cold climate can use roughly 2,500 watts. A window-unit air-conditioner typically uses 1,500 watts, while a central-air system will use about 5 to 20 kilowatts. At 350 degrees Fahrenheit, an electric oven will use 2 kilowatts, while a dishwasher will use about 3.5 kilowatts. Here’s an interesting comparison for you. A desktop computer with a 17-inch cathode-ray-tube monitor uses between 150 and 350 watts, while a computer and monitor in sleep mode only uses 20 watts or less. On the really low end, a clock radio uses just 4 watts. Since a 9-volt alkaline battery stores a total of about 18,000 joules, or about 5 watt-hours, one battery would power your clock-radio for a little more than an hour.
地球上生活着超过65亿人口，我们每年消耗的能量约为5×10²⁰焦耳。在欧佩克石油禁运40年后，85%的能源仍然来自化石燃料：煤炭、石油和天然气。美国人口仅略超过3亿，占世界人口的二十分之一，却消耗了全球五分之一的能源。我们无法回避这个问题：我们是能源消耗者，而且是巨大的能源消耗者。正因如此，我非常高兴奥巴马总统任命诺贝尔物理学奖得主朱棣文担任能源部长。如果我们想要解决能源问题，就必须重视能源物理学。
There are more than 6.5 billion people living on Earth, and we are using about 5 × 1020 joules of energy per year. Forty years after the OPEC oil embargo, 85 percent still comes from fossil fuels: coal, oil, and natural gas. The United States, with only a little more than 300 million residents, one-twentieth of the world population, is responsible for one-fifth of world energy usage. There’s no way to get around this: we are energy spoilers, big energy spoilers. That’s one reason I was so happy that President Obama appointed a Nobel Prize–winning physicist, Steven Chu, as his secretary of energy. If we’re going to solve our energy problems, we’re going to need to pay attention to the physics of energy.
例如，人们对太阳能的潜力寄予厚望，我也非常赞成大力开发太阳能。但我们必须意识到我们所面临的局限性。毫无疑问，太阳是一个绝佳的能源。它每秒产生 4 × 10²⁶瓦（即 4 × 10²⁶焦耳）的能量，其中大部分是可见光和红外线。由于我们知道地球和太阳之间的距离（1.5 亿公里），我们可以计算出有多少能量到达地球。大约是 1.7 × 10¹⁷瓦，或每年约 5 × 10²⁴焦耳。如果你将一块一平方米的太阳能电池板直接对准太阳（假设没有云！），这块电池板大约会接收到 1200 瓦的能量（这里我假设大约 15% 的入射能量会被地球大气层反射和吸收）。一个容易计算的数字是：在没有云的情况下，直接对着太阳照射的每平方米需要 1000 瓦（1 千瓦）。
For example, there is much hope being placed in the potential for solar energy, and I am all for developing it vigorously. But we must beware of the limitations we are up against. There is no question that the Sun is a wonderful source of energy. It produces 4 × 1026 watts—4 × 1026 joules per second—of power, most of it in visible light and in the infrared part of the spectrum. Since we know the distance between the Earth and the Sun (150 million kilometers), we can calculate how much of that power reaches the Earth. It’s about 1.7 × 1017 watts, or about 5 × 1024 joules per year. If you point a one-square-meter panel directly at the Sun (no clouds!), that panel would receive roughly 1,200 watts (I have assumed here that about 15 percent of the incoming power is reflected and absorbed by the Earth’s atmosphere). An easy number to work with is 1,000 watts (1 kilowatt) per square meter pointed directly at the Sun in the absence of clouds.
太阳能的潜力似乎非常巨大。要收集足够的太阳能来满足世界能源需求，大约需要2× 10¹⁰平方米的土地。这大约是我祖国荷兰面积的五倍——而荷兰其实并不是一个很大的国家。
The potential for solar power would seem tremendous. It would take about 2 × 1010 square meters to harvest enough solar energy for the world’s energy needs. That’s about five times the area of my home country, Holland—not a very big country at all.
然而，这里有个问题。昼夜交替，我们还没有考虑到。我们一直以为太阳永远都在那里。云层也会影响太阳能板的接收。如果你的太阳能板不能移动，就无法始终对准太阳。你所在的地理位置也很重要。赤道附近的国家接收到的能量更多（毕竟它们更热），而北半球的北部国家和南半球的南部国家则较少。
However, there is a catch. There are day and night, which we haven’t allowed for yet. We just assumed that the Sun was always there. There are clouds, too. And if your solar panels are not movable, then they cannot remain pointed at the Sun all the time. Where you are situated on the Earth also matters. Countries at the equator receive more energy (they are hotter, after all) than more northern countries (in the Northern Hemisphere) or more southern ones (in the Southern Hemisphere).
接下来，我们需要考虑太阳能收集装置的效率。目前有很多不同的技术，而且还在不断涌现，但实用硅太阳能电池（而非使用昂贵材料制成的太阳能电池）的最高效率约为18%。如果直接利用太阳能加热水（无需先将其转化为电能），效率会高得多。相比之下，即使是不太新的燃油炉，也能轻松达到75%到80%的效率。因此，如果将所有这些限制因素都考虑在内，所需的面积将达到约1万亿平方米，约40万平方英里，大约是德国面积的三倍。而且，我们甚至还没有考虑建造收集和转换所有太阳能的阵列的成本。目前，从太阳中提取电力的成本大约是从化石燃料中提取电力的两倍。不仅转向太阳能的成本会非常惊人，而且这样的项目也远远超出了我们目前的技术能力和政治意愿。这就是为什么在未来一段时间内，太阳能发电在世界经济中将扮演越来越重要但相对较小的角色。
Then we need to take into account the efficiency of the units with which you capture the solar energy. There are lots of different technologies, more all the time, but the maximum efficiency of practical silicon solar cells (as opposed to those made with expensive materials) is about 18 percent. If you use solar energy to directly heat water (without first converting it to electric energy), the efficiency is much higher. An oil-fired furnace, by comparison, even one that’s not so new, can easily reach an efficiency of 75 to 80 percent. So if you take all those limiting factors into account, you would need an area more like a trillion square meters, roughly 400,000 square miles, an area about three times larger than Germany. And we haven’t even considered the cost of building the arrays to collect and convert all that solar power to electricity. At the moment it costs about twice as much to extract electricity from the Sun as it does to extract it from fossil fuels. Not only would the cost of converting to solar power be staggering, such a project is simply beyond our present technological capability or political will. That’s why solar power will play a growing but relatively small role in the world economy for some time.
另一方面，如果我们现在就开始行动，未来四十年我们就能取得巨大进步。绿色和平组织和国际能源署在2009年估计，如果政府提供巨额补贴，太阳能发电到2030年可以满足“全球高达7%的电力需求，到2050年可以满足四分之一的电力需求”。《科学美国人》杂志几年前就指出，一项紧急计划以及未来四十年超过4000亿美元的补贴，可以让太阳能发电满足美国69%的电力需求，以及35%的能源总需求。
On the other hand, if we start now, we could make enormous strides in the next four decades. Greenpeace International and the International Energy Agency estimated in 2009 that with very substantial government subsidies, solar power could meet “up to 7 percent of the world’s power needs by 2030 and fully one-quarter by 2050.” Scientific American magazine argued several years ago that a crash program and more than $400 billion in subsidies over the next forty years could result in solar power providing 69 percent of the United States’ electricity, and 35 percent of its total energy needs.
风力发电怎么样？毕竟，风力发电已经使用了很长时间。就像人类扬帆起航一样，风车的历史远比电力悠久，或许早了一千年之久。无论是在十三世纪的中国，还是更古老的伊朗，亦或是十二世纪的欧洲，从自然界获取能量并将其转化为人类可用能源的原理都完全相同。在所有这些地方，风车都帮助人们完成了一些最艰巨的任务：提水饮用或灌溉农作物，或者用大石头磨谷物制成面粉。无论是否发电，驱动风车都需要风能。
What about wind power? After all, wind power has been used as long as humans have put sails into the wind. Windmills have been around way longer than electric power, maybe even a thousand years longer. And the principle of getting energy from nature and converting it into a different kind of energy for human use was exactly the same, whether it was in thirteenth-century China, even more ancient Iran, or twelfth-century Europe. In all of these places windmills helped do some of the hardest chores human beings took on: lifting water for drinking or crop irrigation, or grinding grains between large stones in order to make flour. It takes wind energy to power a windmill, whether or not it’s making electricity.
作为一种电力生产方式，风能资源丰富、完全可再生，且不产生温室气体排放。2009年，全球风能发电量为340太瓦时（1太瓦时等于1万亿瓦时），约占全球电力消耗的2%。而且，风能发电量正快速增长；事实上，过去三年里，风能发电量已经翻了一番。
As a producer of electricity, wind energy is readily available, utterly renewable, and produces no greenhouse gas emission. In 2009, wind energy production worldwide was 340 terawatt-hours (a terawatt-hour is one trillion watt-hours), which is about 2 percent of the world’s electric consumption. And it is growing rapidly; in fact, electricity production from wind has doubled in the past three years.
那么核能呢？核能的储量远比我们通常认为的要丰富得多。事实上，它无处不在，每天都在我们身边。窗户玻璃中含有放射性钾-40，它的半衰期长达12亿年，其衰变产生的能量有助于加热地核。大气中的所有氦气都是由地球内部天然存在的同位素发生放射性衰变产生的。我们所说的α衰变，实际上是较大的不稳定原子核释放出一个氦原子核的过程。
What about nuclear energy? Nuclear energy is much more plentiful than we are generally aware. It is, in fact, all around us, every day. Window glass contains radioactive potassium-40, which has a half-life of 1.2 billion years, and energy produced by its decay helps to heat the Earth’s core. All the helium in the atmosphere was produced by the radioactive decay of naturally occurring isotopes in the Earth. What we call alpha decay is in fact the emission of a helium nucleus from a larger unstable nucleus.
我收藏了一批非常特别、数量也相当多的Fiestaware餐具，这是一种美国餐具——包括盘子、碗、碟子和杯子——从20世纪30年代开始设计和生产。我喜欢带一些这样的盘子到课堂上给学生们展示。尤其是那些橙色的盘子，被称为“Fiesta红”，它们含有氧化铀，因为氧化铀是陶瓷釉料的常用成分。我把盘子靠近盖革计数器，计数器开始快速发出哔哔声。盘子中的铀会释放伽马射线，这是由于我们称之为裂变的过程，而裂变正是驱动核反应堆的原理。演示结束后，我总是……我邀请学生来我家吃饭，但奇怪的是，从来没有人响应。
I have a very special, very large collection of Fiestaware, which is American tableware—dishes, bowls, saucers, and cups—designed and manufactured starting in the 1930s. I love to bring a few of these plates into class and show them to my students. The orange ones, in particular, which are called “Fiesta red,” have uranium oxide in them, since it was a common ingredients in ceramic glazes. I hold a plate near a Geiger counter, and it begins to beep rapidly. The uranium in the plate emits gamma rays as a result of the process we call fission, which is the same process that drives nuclear reactors. After this demonstration, I always invite students to come to dinner at my home, but strangely I have never gotten any takers.
核裂变，即重原子核的分裂，能够产生大量的能量。无论是在核反应堆中，链式反应分裂铀-235原子核的过程受到控制；还是在原子弹中，链式反应不受控制，造成巨大的破坏，核裂变都能产生大量的能量。一座每秒产生约10亿焦耳（10⁹瓦，或1000兆瓦）能量的核电站，一年大约消耗10²⁷个铀-235原子核，相当于约400公斤铀-235。
Fission, or splitting of heavy nuclei, generates large amounts of energy, whether in a nuclear reactor, in which the chain reactions splitting uranium-235 nuclei are controlled, or in an atomic bomb, in which the chain reactions are uncontrolled and produce tremendous destruction. A nuclear power plant that produces about a billion joules per second (109 watts, or 1,000 megawatts) consumes about 1027 uranium-235 nuclei in a year, which amounts to only about 400 kilograms of uranium-235.
然而，天然铀中只有0.7%是铀-235（99.3%是铀-238）。因此，核电站使用浓缩铀；浓缩程度各不相同，但通常为5%。这意味着，核电站的铀燃料棒中铀-235的含量不是0.7%，而是5%。因此，一座1000兆瓦的核反应堆每年大约消耗8000公斤铀，其中约400公斤是铀-235。相比之下，一座1000兆瓦的化石燃料发电厂每年大约消耗50亿公斤煤。
However, only 0.7 percent of natural uranium consists of uranium 235 (99.3 percent is uranium-238). Therefore, nuclear power plants use enriched uranium; the degree of enrichment varies, but a typical number is 5 percent. This means that instead of 0.7 percent uranium-235, their uranium fuel rods contain 5 percent uranium-235. Thus a 1,000-megawatt nuclear reactor will consume about 8,000 kilograms of uranium per year, of which about 400 kilograms is uranium-235. In comparison, a 1,000-megawatt fossil-fuel power plant will consume about 5 billion kilograms of coal per year.
铀浓缩成本高昂，需要数千台离心机。武器级铀的铀-235含量至少达到85%。现在你或许明白为什么世界各国如此担忧那些铀浓缩程度不明且无法核实的国家了吧！
The enrichment of uranium is costly; it’s done with thousands of centrifuges. Weapons-grade uranium is enriched to at least 85 percent uranium-235. Perhaps you now understand why the world is very worried about countries that enrich uranium to an unspecified degree that cannot be verified!
在核电站中，受控链式反应产生的热量将水转化为蒸汽，蒸汽驱动汽轮机发电。核电站将核能转化为电能的效率约为35%。如果你看到新闻报道说一座核电站发电1000兆瓦，你并不知道这1000兆瓦是指总功率（其中1/3转化为电能，2/3以热能的形式散失），还是指全部电能。如果是后者，那么该电站的总功率约为3000兆瓦。这差别很大！我昨天在新闻上看到，伊朗即将……投产一座核电站，发电量为 1000 兆瓦（这话说得很清楚！）。
In nuclear power plants, the heat produced by the controlled chain reactions turns water into steam, which then drives a steam turbine, producing electricity. A nuclear power plant’s efficiency converting nuclear energy into electricity is about 35 percent. If you read that a nuclear power plant produces 1,000 megawatts, you do not know whether it is 1,000 megawatts total power (of which 1/3 is converted to electrical energy and of which 2/3 is lost as heat), or whether it’s all electric power in which case the total plant’s power is about 3,000 megawatts. It makes a big difference! I read yesterday in the news that Iran is shortly going to put on line a nuclear power plant that will produce 1,000 megawatts of electricity (that’s clear language!).
近年来，随着人们对全球变暖的担忧急剧增加，核能再次成为热门选择——与燃烧化石燃料的发电厂不同，核电站几乎不排放温室气体。美国目前已有超过一百座核电站，发电量约占美国能源消耗的20%。在法国，这一比例约为75%。在全球范围内，核电站产生的电力约占全球总发电量的15%。各国对核电的政策各不相同，但由于三里岛和切尔诺贝利核事故引发的恐慌，建造更多核电站需要大量的政治游说。此外，核电站的建设成本也非常高昂：据估计，美国每座核电站的造价在50亿至100亿美元之间，而中国则约为20亿美元。最后，核电站放射性废物的储存仍然是一个巨大的技术和政治难题。
As concern about global warming has increased dramatically in the past few years, the nuclear energy option is coming back into fashion—unlike power plants burning fossil fuels, nuclear plants don’t emit much in the way of greenhouse gases. There are already more than a hundred nuclear power plants in the United States, producing about 20 percent of the energy we consume. In France this number is about 75 percent. Worldwide, about 15 percent of the total electric energy consumed is produced in nuclear plants. Different countries have different policies regarding nuclear power, but building more plants will require a great deal of political persuasion due to the fear generated by the infamous nuclear accidents at Three Mile Island and Chernobyl. The plants are also very expensive: estimates range from $5 to $10 billion per plant in the United States, and around $2 billion in China. Finally, storing the radioactive waste from nuclear plants remains an enormous technological and political problem.
当然，地球上仍然蕴藏着大量的化石燃料，但我们消耗它们的速度远远超过了自然界生成它们的速度。世界人口持续增长，而许多增长最快的国家，例如中国和印度，正以惊人的速度推进高耗能发展。因此，我们别无选择，我们正面临着非常严重的能源危机。我们应该如何应对？
Of course, we still have massive amounts of fossil fuel on Earth, but we are using it up much, much faster than nature can create it. And the world population continues to grow, while energy-intensive development is proceeding at an extremely rapid clip in many of the largest growth countries, like China and India. So there really is no way around it. We have a very serious energy crisis. What should we do about it?
嗯，很重要的一点是，我们要更加意识到自己每天究竟消耗了多少能源，并尽量减少能源消耗。我认为我自己的能源消耗量相当低，不过由于我住在美国，我肯定我的能源消耗量是世界平均水平的四到五倍。我用电；我用燃气供暖和热水；我用燃气做饭。我开车——开得不多，但确实会消耗一些汽油。把这些加起来，我认为我（2009年）平均每天消耗大约1亿焦耳（30千瓦时）的能源，其中大约一半是电能。这相当于雇佣大约两百个奴隶像狗一样每天为我工作12个小时。想想看……没错。在古代，只有最富有的皇室成员才能过上这样的生活。我们生活在一个多么奢华、多么不可思议的时代啊！两百名奴隶每天为我工作十二个小时，不停歇，这一切都是为了让我能够过上现在这样的生活。一千瓦时（360万焦耳）的电，我只需支付25美分。所以，我为这两百名奴隶支付的全部能源费用（我把汽油和天然气也算进去了，因为它们的单位能量价格相差不大）平均每月大约225美元；也就是说，每个奴隶每月大约1美元！因此，改变观念至关重要。但这只能解决部分问题。
Well, one important thing is to become more aware of just how much energy we use every day, and to use less. My own energy consumption is quite modest, I think, although since I live in the United States, I’m sure I also consume four or five times more than the average person in the world. I use electricity; I heat my house and water with gas, and I cook with gas. I use my car—not very much, but I do use some gasoline. When I add that all up, I think I consumed (in 2009) on average about 100 million joules (30 kilowatt-hours) per day, of which about half was electrical energy. This is the energy equivalent of having about two hundred slaves working for me like dogs twelve hours a day. Think about that. In ancient times only the richest royalty lived like this. What luxurious, incredible times we live in. Two hundred slaves are working for me every single day, twelve hours a day without stopping, all so that I can live the way I live. For 1 kilowatt-hour of electricity, which is 3.6 million joules, I pay a mere 25 cents. So my entire energy bill (I included gas and gasoline, as their price per unit energy is not very different) for those two hundred slaves was, on average, about $225 a month; that’s about $1 per slave per month! So a change of consciousness is vital. But that will only get us so far.
改变使用习惯，例如用节能灯（紧凑型荧光灯）代替白炽灯，可以带来巨大的改变。我亲眼见证了这种改变带来的显著效果。2005年，我家（剑桥）的用电量为8860千瓦时，2006年为8317千瓦时。这些用电量用于照明、空调、洗衣机和烘干机（热水、烹饪和供暖使用燃气）。2006年12月中旬，我的儿子查克（他是新一代能源公司的创始人）送给我一份特别的礼物。他把家里所有的白炽灯泡（一共75个）都换成了荧光灯泡。 2007年我的用电量大幅下降至5251千瓦时，2008年降至5184千瓦时，2009年降至5226千瓦时。用电量减少了40%，使我每年的电费节省了约850美元。鉴于照明用电量约占美国居民用电量的12%，商业用电量的25%，这显然是正确的做法！
Changing habits to use more energy-conserving devices, such as compact fluorescent lights (CFLs) instead of incandescent lights, can make a large difference. I got to see the change I could make in quite a dramatic fashion. My electric consumption at my home in Cambridge was 8,860 kilowatt-hours in 2005 and 8,317 kilowatt-hours in 2006. This was for lighting, air-conditioning, my washing machine, and the dryer (I use gas for hot water, cooking, and heating). In mid-December of 2006, my son, Chuck (who is the founder of New Generation Energy), gave me a wonderful present. He replaced all the incandescent lightbulbs (a total of seventy-five) in my house with fluorescent bulbs. My electricity consumption dropped dramatically in 2007 to 5,251 kilowatt-hours, 5,184 kilowatt-hours in 2008, and 5,226 kilowatt-hours in 2009. This 40 percent reduction in my electricity consumption lowered my yearly bill by about $850. Since lighting alone accounts for about 12 percent of U.S. residential electric energy use and 25 percent of commercial use, it’s clearly the way to go!
澳大利亚政府也采取了类似的措施，于2007年开始制定计划，用荧光灯泡替换全国所有的白炽灯泡。这不仅能大幅减少澳大利亚的温室气体排放，还能降低每个家庭的能源账单（就像我家一样）。不过，我们仍需做得更多。
Following a similar path, the Australian government started to make plans in 2007 to replace all incandescent lightbulbs in the country with fluorescent ones. This would not only substantially reduce Australia’s greenhouse gas emission, but it would also reduce energy bills in every household (as it did in mine). We still need to do more, though.
我认为，我们要想在维持目前生活质量的前提下生存下去，唯一的办法就是发展核聚变，将其作为一种可靠、重要的能源来源。而不是核裂变——也就是利用铀和钚。原子核分裂成碎片并释放能量，为核反应堆提供动力——而聚变，即氢原子聚合形成氦原子并释放能量的过程，则是恒星和热核炸弹的能量来源。聚变是我们所知的单位质量能量产生能力最强的过程——除了物质与反物质碰撞（反物质碰撞没有产生能量的潜力）。
I think the only way that we might survive while keeping anything like our current quality of life is by developing nuclear fusion as a reliable, serious energy source. Not fission—whereby uranium and plutonium nuclei break up into pieces and emit energy, which powers nuclear reactors—but fusion, in which hydrogen atoms merge together to create helium, releasing energy. Fusion is the process that powers stars—and thermonuclear bombs. Fusion is the most powerful energy-producing process per unit of mass we know of—except for matter and antimatter colliding (which has no potential for energy generation).
由于一些相当复杂的原因，只有某些类型的氢（氘和氚）才适合用于聚变反应堆。氘（其原子核包含一个中子和一个质子）储量丰富；地球上每六千个氢原子中就有一个是氘。由于海洋中大约有十亿立方千米的水，氘的供应几乎是无限的。地球上没有天然存在的氚（它具有放射性，半衰期约为十二年），但它很容易在核反应堆中生产。
For reasons that are quite complicated, only certain types of hydrogen (deuterium and tritium) are well suited for fusion reactors. Deuterium (whose nucleus contains one neutron as well as one proton) is readily available; about one in every six thousand hydrogen atoms on Earth is deuterium. Since we have about a billion cubic kilometers of water in our oceans, the supply of deuterium is pretty much unlimited. There is no naturally occurring tritium on Earth (it’s radioactive with a half life of about twelve years), but it is easily produced in nuclear reactors.
真正的问题在于如何制造一个功能完善、实用且可控的聚变反应堆。我们能否成功实现这一点，目前尚不明朗。为了使氢原子核发生聚变，我们需要在地球上创造出接近1亿摄氏度的高温，这相当于恒星核心的温度。
The real problem is how to create a functioning, practical, controlled fusion reactor. It’s not at all clear that we will ever succeed in doing so. In order to get hydrogen nuclei to fuse, we need to create, here on Earth, temperatures in the 100-million-degree range, approximating the temperature at the core of stars.
科学家们多年来一直在努力研究核聚变——而且我认为，随着越来越多的政府似乎真正意识到能源危机的存在，他们现在在这方面投入了更多精力。这无疑是个大问题。但我是一个乐观主义者。毕竟，在我职业生涯中，我见证了本领域发生的翻天覆地的变化，这些变化彻底颠覆了我们对宇宙的认知。例如，宇宙学曾经主要靠推测和少量科学研究，如今已发展成为一门真正的实验科学，我们对宇宙的起源有了大量的了解。事实上，我们现在正生活在许多人所说的宇宙学的黄金时代。
Scientists have been working hard on fusion for many years—and I think they are working harder on it now that more and more governments seem genuinely convinced that the energy crisis is real. It’s a big problem, for sure. But I’m an optimist. After all, in my professional lifetime I’ve seen changes in my field that have been absolutely mind-blowing, turning our notions of the universe upside down. Cosmology, for instance, which used to be mostly speculation and a little bit of science, has now become a genuine experimental science, and we know an enormous amount about the origins of our universe. In fact, we now live in what many call the golden age of cosmology.
当我开始从事X射线天文学研究时，我们只知道深空中大约有十几个X射线源。现在我们知道的已经成千上万个了。五十年前，你那台四磅重的笔记本电脑的计算能力，就足以占据我所在的麻省理工学院大楼的大部分空间。五十年前，天文学家只能依靠地面光学和射电望远镜——仅此而已！如今，我们不仅拥有哈勃太空望远镜，还拥有一系列X射线卫星天文台、伽马射线天文台，而且我们还在使用和建造新的中微子天文台！五十年前，就连宇宙大爆炸的可能性都尚未定论。而现在，我们不仅认为我们知道宇宙在大爆炸后最初百万分之一秒的模样，而且还能自信地研究超过130亿年历史的天体，这些天体形成于宇宙大爆炸后的最初5亿年。在这些巨大的发现和变革的背景下，我怎能不相信科学家们终将解决受控核聚变的问题呢？我不想轻视其中的困难，也不想轻视尽快实现这一目标的重要性，但我相信这只是时间问题。
When I began to do research in X-ray astronomy, we knew of about a dozen X-ray sources in deep space. Now we know of many tens of thousands. Fifty years ago the computing capacity in your four-pound laptop would have taken up most of the building at MIT where I have my office. Fifty years ago astronomers relied on ground-based optical and radio telescopes—that was it! Now we not only have the Hubble Space Telecope, we’ve had a string of X-ray satellite observatories, gamma ray observatories, and we’re using and building new neutrino observatories! Fifty years ago even the likelihood of the big bang was not a settled issue. Now we not only think we know what the universe looked like in the first one-millionth of a second after the big bang—we confidently study astronomical objects more than 13 billion years old, objects formed in the first 500 million years after the explosion that created our universe. Against the backdrop of these immense discoveries and transformations, how can I not think scientists will solve the problem of controlled fusion? I don’t want to trivialize the difficulties, or the importance of doing so soon, but I do believe it’s only a question of time.
第十章
CHAPTER 10
来自外太空的X射线！
X-rays from Outer Space!
苍穹日夜不停地挑战着人类，促使我们去理解周遭的世界，这也是物理学家们一直对天文学着迷的原因之一。“太阳是什么？”我们不禁会问。“它为什么会运动？”月亮、行星和恒星又是什么呢？想想我们的祖先花了多少心思才弄明白行星与恒星的不同；它们围绕太阳运行；而且这些轨道是可以观测、绘制、解释和预测的。十六、十七世纪许多最伟大的科学家——包括尼古拉·哥白尼、伽利略·伽利雷、第谷·布拉赫、约翰内斯·开普勒和艾萨克·牛顿——都曾仰望星空，试图解开这些夜幕下的谜团。想象一下，当伽利略将望远镜对准木星——当时它不过是一个光点——并发现围绕它运行的四颗小卫星时，他该是多么激动！与此同时，对于他们来说，对夜复一夜出现的繁星知之甚少，该是多么令人沮丧啊。值得注意的是，古希腊的德谟克利特以及十六世纪的天文学家乔尔丹诺·布鲁诺都曾提出，这些星星就像我们的太阳一样，但当时并没有证据来证明这一点。没错。它们会是什么？是什么让它们悬在空中？它们离我们有多远？为什么有些比其他更亮？为什么它们有不同的颜色？在晴朗的夜晚，从地平线一端延伸到另一端的那条宽阔的光带又是什么？
The heavens have always provided a daily and nightly challenge to human beings seeking to understand the world around us, which is one reason physicists have always been entranced by astronomy. “What is the Sun?” we wonder. “Why does it move?” And what about the Moon, the planets, and the stars? Think about what it took for our ancestors to figure out that the planets were different from the stars; that they orbited the Sun; and that those orbits could be observed, charted, explained, and predicted. Many of the greatest scientific minds of the sixteenth and seventeenth centuries—among them Nicolaus Copernicus, Galileo Galilei, Tycho Brahe, Johannes Kepler, Isaac Newton—were compelled to turn their gaze to the heavens to unlock these nightly mysteries. Imagine how exciting it must have been for Galileo when he turned his telescope toward Jupiter, barely more than a point of light, and discovered four little moons in orbit around it! And, at the very same time, how frustrating it must have been to them to know so little about the stars that came out night after night. Remarkably, the ancient Greek Democritus as well as the sixteenth-century astronomer Giordano Bruno proposed that the stars are like our own Sun, but there was no evidence to prove them right. What could they be? What held them in the sky? How far away were they? Why were some brighter than others? Why did they have different colors? And what was that wide band of light reaching from one horizon to the other on a clear night?
自那时起，天文学和天体物理学的发展历程就是不断探索并解答这些问题，以及在我们开始找到一些答案后涌现出的其他问题。在过去的四百多年里，天文学家所能观测到的天体当然取决于望远镜的功率和灵敏度。但第谷·布拉赫是个例外，他使用非常简单的设备，仅凭肉眼就进行了非常详细的观测，这使得开普勒得以得出三大重大发现，即现在为人所知的开普勒定律。
The story of astronomy and astrophysics since those days has been the quest to answer those questions, and the additional questions that arose when we started to come up with some answers. For the last four hundred years or so, what astronomers have been able to see, of course, has depended on the power and sensitivity of their telescopes. The great exception was Tycho Brahe, who made very detailed observations with the naked eye, using very simple equipment, that allowed Kepler to arrive at three major discoveries, now known as Kepler’s laws.
在那段时间的大部分时间里，我们只有光学望远镜。我知道这对于非天文学家来说听起来很奇怪。一听到“望远镜”，你首先想到的肯定是“装有透镜和镜子的管子，你可以对着它观察”，对吧？望远镜怎么可能不是光学的呢？2009年10月，奥巴马总统主持了一场天文之夜活动，白宫草坪上架设了许多望远镜，而每一台都是光学望远镜。
For most of that time all we had were optical telescopes. I know that sounds odd to a non-astronomer. When you hear “telescope,” you think, automatically, “tube with lenses and mirrors that you peer into,” right? How could a telescope not be optical? When President Obama hosted an astronomy night in October 2009, there were a bunch of telescopes set up on the White House lawn, and every single one of them was an optical telescope.
自20世纪30年代卡尔·扬斯基发现来自银河系的无线电波以来，天文学家一直在努力拓宽观测宇宙的电磁辐射范围。他们搜寻并发现了微波辐射（高频无线电波）、红外线和紫外线辐射（频率略低于和略高于可见光）、X射线和伽马射线。为了探测这些辐射，我们开发了许多专门设计的望远镜——其中一些是X射线和伽马射线卫星——使我们能够更深入、更广泛地观测宇宙。甚至还有一些中微子望远镜位于地下，包括目前正在南极建造的“冰立方”（IceCube），这个名字可谓名副其实。
But ever since the 1930s, when Karl Jansky discovered radio waves coming from the Milky Way, astronomers have been seeking to broaden the range of electromagnetic radiation through which they observe the universe. They have hunted for (and discovered) microwave radiation (high-frequency radio waves), infrared and ultraviolet radiation (with frequencies just below and just above those of visible light), X-rays, and gamma rays. In order to detect this radiation, we’ve developed a host of specially designed telescopes—some of them X-ray and gamma ray satellites—enabling us to see more deeply and broadly into the universe. There are even neutrino telescopes underground, including one being built right now at the South Pole, called, appropriately enough, IceCube.
在过去的四十五年里——也就是我从事天体物理学研究的四十五年里——我一直致力于X射线天文学领域的研究：发现新的X射线源。并致力于解释我们观察到的众多不同现象。正如我之前所写，我的职业生涯始于该领域令人兴奋的早期阶段，并在接下来的四十年里一直身处其中。X射线天文学改变了我的人生，但更重要的是，它改变了天文学本身的面貌。本章及接下来的四章将带您游览X射线宇宙，而我将以一位毕生致力于该领域研究和探索的科学家的视角，为您呈现这段旅程。让我们从X射线本身开始吧。
For the last forty-five years—my life in astrophysics—I have been working in the field of X-ray astronomy: discovering new X-ray sources and developing explanations for the many different phenomena we observe. As I wrote earlier, the beginning of my career coincided with the heady and exciting early years of the field, and I was in the thick of things for the next four decades. X-ray astronomy changed my life, but more important, it changed the face of astronomy itself. This chapter and the four that follow will take you on a tour of the X-ray universe, from the standpoint of someone who’s worked and lived in that universe for his entire scientific career. Let’s start with X-rays themselves.
什么是X射线？
What Are X-rays?
X射线的名字听起来很奇特，之所以得此名，是因为它们“未知”（就像方程式中的x一样），但它们其实只是光子——电磁辐射——构成了我们肉眼无法看到的电磁波谱中介于紫外线和伽马射线之间的部分。在荷兰语和德语中，它们不被称为X射线；而是以发现它们的德国物理学家威廉·伦琴的名字命名，他于1895年发现了X射线。我们区分X射线的方式与区分该波谱中的其他粒子的方式相同，主要有三种不同但又相互关联的方式：频率（每秒的周期数，单位为赫兹）、波长（单个波的长度，单位为米，在本例中为纳米）或能量（单位为电子伏特，eV，或千电子伏特，keV）。
X-rays have an exotic-sounding name, which they received because they were “unknown” (like the x in an equation), but they are simply photons—electromagnetic radiation—making up the portion of the electromagnetic spectrum that we cannot see between ultraviolet light and gamma rays. In Dutch and in German they are not called X-rays; instead they are named after the German physicist, Wilhelm Röntgen, who discovered them in 1895. We distinguish them the same way we identify other inhabitants of that spectrum, in three different but connected ways: by frequency (the number of cycles per second, expressed in hertz), by wavelength (the length of an individual wave, in meters, in this case nanometers), or by energy (in electron volts, eV, or thousands of electron volts, keV).
以下是一些简单的比较。绿光的波长约为500纳米（500亿分之一米），能量约为2.5电子伏特。能量最低的X射线光子能量约为100电子伏特，是绿光光子能量的40倍，波长约为12纳米。能量最高的X射线能量约为100千电子伏特，波长约为0.012纳米。（牙医使用的X射线能量最高约为50千电子伏特。）在电磁波谱的另一端，美国的广播电台在调幅（AM）波段进行广播，频率范围在520千赫兹（波长577米，约三分之一英里）到1710千赫兹（波长175米，几乎是绿光光子的两倍）之间。（长度相当于一个足球场）。它们的能量比绿光低十亿倍，比X射线低万亿倍。
Here are some quick points of comparison. Green light has a wavelength of about 500 billionths of a meter, or 500 nanometers, and an energy of about 2.5 electron volts. The lowest-energy X-ray photon is about 100 eV, forty times the energy of a photon of green light, with a wavelength of about 12 nanometers. The highest-energy X-rays are about 100 keV, with wavelengths of about 0.012 nanometers. (Your dentist uses X-rays up to about 50 keV.) At the other end of the electromagnetic spectrum, in the United States, radio stations broadcast in the AM band between 520 kilohertz (wavelength 577 meters—about a third of a mile) and 1,710 kilohertz (wavelength 175 meters—nearly twice the length of a football field). Their energy is a billion times less than green light, and a trillion times less than X-rays.
自然界以多种方式产生X射线。大多数放射性原子在核衰变过程中会自然释放X射线。具体来说，就是电子从高能级跃迁到低能级；能量差可以以X射线光子的形式释放出来。由于电子的能级是量子化的，这些光子的能量非常离散。或者，当电子高速掠过原子核时，它们会改变方向，并以X射线的形式释放部分能量。这种X射线发射现象在天文学以及任何医疗或牙科X光机中都非常常见，我们称之为“轫致辐射”（bremsstrahlung），这是一个比较拗口的德语名称，字面意思是“制动辐射”。这里有一些关于轫致辐射X射线产生的动画演示：www.youtube.com/watch?v =3fe6rHnhkuY 。一些医用X射线机也能产生离散能量的X射线，但通常轫致辐射（产生连续的X射线光谱）占主导地位。当高能电子围绕磁力线螺旋运动时，它们的运动方向会不断变化，因此它们也会以X射线的形式辐射出一部分能量；我们称之为同步辐射，但它也被称为磁轫致辐射（这就是蟹状星云中正在发生的事情——见下文）。
Nature creates X-rays in a number of different ways. Most radioactive atoms emit them naturally during nuclear decay. What happens is that electrons jump down from a higher energy state to a lower one; the difference in energy can be emitted as an X-ray photon. These photons have very discrete energies as the energy levels of the electrons are quantized. Or, when electrons pass by atomic nuclei at high speeds, they change direction and emit some of their energy in the form of X-rays. We call this kind of X-ray emission, which is very common in astronomy as well as in any medical or dental X-ray machine, a difficult German name, bremsstrahlung, which literally means “braking radiation.” There are some helpful animated versions of bremsstrahlung X-ray production here: www.youtube.com/watch?v=3fe6rHnhkuY. X-rays of discrete energies can also be produced in some medical X-ray machines, but in general the bremsstrahlung (which produces a continuous X-ray spectrum) dominates. When high-energy electrons spiral around magnetic field lines, the direction of their speed changes all the time and they will therefore also radiate some of their energy in the form of X-rays; we call this synchrotron radiation, but it’s also called magnetic bremsstrahlung (this is what is happening in the Crab Nebula—see below).
自然界在将高密度物质加热到极高温度（数百万开尔文）时也会产生X射线。我们称之为黑体辐射（参见第14章）。物质只有在非常极端的情况下才会达到如此高的温度，例如超新星爆发——一些大质量恒星壮观的死亡爆炸——或者气体以极高的速度落向黑洞或中子星（更多内容请参见第13章，敬请期待！）。例如，太阳表面温度约为6000开尔文，其辐射能量中只有不到一半（46%）是可见光。其余大部分是红外线（49%）和紫外线（5%）辐射。太阳的温度远不足以发射X射线。太阳确实会发射一些X射线，其物理机制尚未完全明了，但X射线辐射的能量仅占总能量的百万分之一左右。它散发的能量。你自身的身体会散发红外辐射（参见第9章）；它的温度不足以发出可见光。
Nature also creates X-rays when it heats dense matter to very, very high temperatures, millions of degrees kelvin. We call this blackbody radiation (see chapter 14). Matter only gets this hot in pretty extreme circumstances, such as supernova explosions—the spectacular death explosions of some massive stars—or when gas falls at very high speeds toward a black hole or neutron star (more on that in chapter 13, promise!). The Sun, for instance, with a temperature of about 6,000 kelvin at its surface, radiates a little less than half its energy (46 percent) in visible light. Most of the rest is in infrared (49 percent) and ultraviolet (5 percent) radiation. It’s nowhere near hot enough to emit X-rays. The Sun does emit some X-rays, the physics of which is not fully understood, but the energy emitted in X-rays is only about one-millionth of the total energy it emits. Your own body emits infrared radiation (see chapter 9); it’s not hot enough to emit visible light.
X射线最有趣也最有用的特性之一是，某些物质，例如骨骼，比其他物质（例如软组织）吸收X射线更多。这就解释了为什么口腔或手部的X光片会呈现明暗区域。如果您做过X光检查，您也一定体验过被铅围裙包裹以保护身体其他部位，因为X射线照射会增加患癌风险。正因如此，我们的大气层能够如此有效地吸收X射线，这在很大程度上是一件好事。在海平面，大约99%的低能量X射线（1千电子伏特）会被1厘米厚的空气吸收。对于5千电子伏特的X射线，大约需要80厘米（近3英尺）厚的空气才能吸收99%的X射线。对于25千电子伏特的高能量X射线，则需要大约80米厚的空气才能吸收相同比例的X射线。
One of the most interesting—and useful—aspects of X-rays is that certain kinds of matter, like bones, absorb X-rays more than others, like soft tissue, which explains why an X-ray image of your mouth or hand shows light and dark areas. If you’ve had an X-ray, you’ve also had the experience of being draped with a lead apron to protect the rest of your body, since exposure to X-rays can also increase your risk of getting cancer. Which is why it’s mostly a good thing that our atmosphere is such a good absorber of X-rays. At sea level about 99 percent of low-energy X-rays (at 1 keV) are absorbed by just 1 centimeter of air. For X-rays at 5 keV, it takes about 80 centimeters of air, nearly three feet, to absorb 99 percent of the X-rays. For high-energy X-rays at 25 keV, it takes about 80 meters of air to absorb the same proportion.
X射线天文学的诞生
The Birth of X-ray Astronomy
现在你明白为什么1959年布鲁诺·罗西萌生了寻找外太空X射线的想法时，会提议使用一枚能够完全飞出大气层的火箭。但他寻找X射线的想法确实有些异想天开。当时并没有任何可靠的理论依据表明太阳系外存在X射线。但罗西毕竟是罗西，他成功说服了他在美利坚科学与工程学院（AS&E）的学生马丁·安尼斯以及他的同事里卡多·贾科尼，让他们相信这个想法值得一试。
Now you understand why, back in 1959, when Bruno Rossi had the idea to go looking for X-rays from outer space, he proposed using a rocket that could get completely outside the atmosphere. But his idea about looking for X-rays was wild. There really were no sound theoretical reasons to think there were X-rays coming from outside the solar system. But Rossi was Rossi, and he convinced his former student Martin Annis at American Science and Engineering (AS&E) and one member of his staff, Riccardo Giacconi, that the idea was worth pursuing.
贾科尼和他的同事弗兰克·保利尼研制出一种特殊的盖革-米勒管，可以探测X射线，并能安装在火箭的鼻锥内。事实上，他们在一枚火箭上安装了三个这样的探测器。他们称之为大面积探测器，但在当时，“大”指的是信用卡大小。美国航空航天工程系（AS&E）的工程师们四处寻求资金来资助这项实验，但NASA拒绝了他们的申请。
Giacconi and his co-worker Frank Paolini developed special Geiger-Müller tubes that could detect X-rays and fit into the nose cone of a rocket. In fact, they put three of them in one rocket. They called them large-area detectors, but large in those days meant the size of a credit card. The AS&E guys went looking for funding to underwrite this experiment, and NASA turned their proposal down.
贾科尼随后修改了方案，将月球也列为目标，并重新提交给了空军剑桥研究实验室。（AFCRL）。他们的论点是，太阳X射线应该会在月球表面产生所谓的荧光发射，这将有助于对月球表面进行化学分析。他们还预期，由于太阳风中电子的撞击，月球表面会产生轫致辐射。由于月球距离地球很近，X射线或许可以被探测到。这是一个非常明智的举措，因为AS&E已经从空军获得了其他几个项目（其中一些是机密项目）的支持，他们可能知道空军对月球很感兴趣。无论如何，这一次提案获得了批准。
Giacconi then changed the proposal by including the Moon as a target and resubmitted it to the Air Force Cambridge Research Laboratories (AFCRL). The argument was that the solar X-rays should produce so-called fluorescent emission from the lunar surface and that this would facilitate chemical analysis of the lunar surface. They also expected bremsstrahlung from the lunar surface due to the impact of electrons present in the solar wind. Since the Moon is so close, X-rays might be detectable. This was a very smart move, as AS&E had already received support from the Air Force for several other projects (some of which were classified), and they may have known that the agency was interested in the Moon. In any event, this time the proposal was approved.
在1960年和1961年两次火箭发射失败后，1962年6月18日午夜前一分钟的发射任务是探测月球X射线，并寻找太阳系外的X射线源。火箭在80公里（超过25万英尺）以上的高度停留了六分钟，在这个高度，盖革-米勒计数管可以探测到能量范围约为1.5-6千电子伏的X射线，且不受大气干扰。这就是当时利用火箭进行太空观测的方式：将火箭送出大气层，让它在空中扫描五六分钟，然后返回地面。
After two rocket failures in 1960 and 1961, the launch one minute before midnight on June 18, 1962, had the stated mission of trying to detect X-rays from the Moon and to search for X-ray sources beyond the solar system. The rocket spent just six minutes above the 80-kilometer mark (over 250,000 feet up), where the Geiger-Müller tubes could detect X-rays in the range from about 1.5–6 keV without atmospheric interference. That’s the way you observed in space with rockets in those days. You sent the rockets out of the atmosphere, where they scanned the skies for only five or six minutes, then they came back down.
真正令人惊讶的是，他们立即发现了 X 射线——不是来自月球，而是来自太阳系外的某个地方。
The truly amazing thing is that right away they found X-rays—not from the Moon, but from someplace outside the solar system.
来自深空的X射线？为什么？当时没人能理解这个发现。在那次飞行之前，我们只知道一颗会发出X射线的恒星——太阳。假设太阳距离我们10光年，这在天文尺度上其实很近，那么那次历史性飞行所使用的设备灵敏度要低一百万倍，根本无法探测到太阳的X射线。这一点人尽皆知。因此，无论这个X射线源位于何处，它发出的X射线强度都必须至少是太阳的百万倍——而且这还是在它距离我们非常近的情况下。产生比太阳高一百万倍甚至十亿倍X射线的天体，在当时是闻所未闻的。而且，当时的物理学也无法描述这样的天体。换句话说，这必定是天体中一种全新的现象。
X-rays from deep space? Why? No one understood the finding. Before that flight we had known of exactly one star that emitted X-rays, our own Sun. And if the Sun had been 10 light-years away, say, which is really just around the corner in astronomical terms, the equipment in that historic flight was a million times too insensitive to detect its X-rays. Everyone knew this. So wherever this source was located, it had to emit at least a million times more X-rays than the Sun—and that was only if it was really close by. Astronomical objects that produced (at least) a million or a billion times more X-rays than the Sun were literally unheard of. And there was no physics to describe such an object. In other words, it had to be a brand new kind of phenomenon in the heavens.
1962年6月18日至19日夜间，一个全新的科学领域诞生了：X射线天文学。
A whole new field of science was born the night of June 18–19, 1962: X-ray astronomy.
天体物理学家开始发射大量装有探测器的火箭，以确定该辐射源的精确位置以及是否存在其他类似辐射源。测量天体位置总是存在不确定性，因此天文学家提出了“误差框”的概念，这是一个贴在天穹上的假想框，其边长以度、角分或角秒来衡量。他们将误差框做得足够大，使得目标物体实际位于框内的概率达到90%。天文学家对误差框如此重视，原因显而易见：误差框越小，物体的位置就越精确。这在X射线天文学中尤为重要，因为误差框越小，就越有可能找到辐射源的光学对应体。因此，将误差框做得非常非常小是一项重大成就。
Astrophysicists began sending up lots of rockets fitted with detectors to figure out precisely where the source was located and whether there were any others. There is always uncertainty in measuring the position of objects in the heavens, so astronomers talk about an “error box,” an imaginary box pasted on the dome of the sky whose sides are measured in degrees, or arc minutes, or arc seconds. They make the box big enough so there is a 90 percent chance that the object is really inside it. Astronomers obsess about error boxes, for obvious reasons; the smaller the box, the more accurate the position of the object. This is especially important in X-ray astronomy, where the smaller the box, the more likely it is that you will be able to find the source’s optical counterpart. So making the box really, really small is a major achievement.
爱丁堡大学的安迪·劳伦斯教授在一个名为“电子天文学家”（The e-Astronomer）的天文博客上发表了一篇回忆录，讲述了他撰写论文时盯着数百张X射线源位置图的经历。“一天晚上，我梦见自己变成了一个误差框，找不到我应该框住的X射线源。我醒来时满头大汗。” 你肯定能理解他的感受！
Professor Andy Lawrence at the University of Edinburgh writes an astronomy blog called The e-Astronomer on which he once posted a reminiscence of working on his thesis, staring at hundreds of position plots of X-ray sources. “One night I dreamt I was an error box, and couldn’t find the X-ray source I was supposed to enclose. I woke up sweating.” You can understand why!
由里卡多·贾科尼、赫伯·古尔斯基、弗兰克·保利尼和布鲁诺·罗西发现的X射线源的误差范围约为10度×10度，即100平方度。要知道，太阳的直径只有半度。确定该射线源位置的不确定性竟然相当于500个太阳的面积！这个误差范围包含了天蝎座和矩尺座的部分区域，并且与天坛座的边界相接。显然，他们无法确定该射线源位于哪个星座。
The size of the error box of the X-ray source discovered by Riccardo Giacconi, Herb Gursky, Frank Paolini, and Bruno Rossi was about 10 degrees × 10 degrees, or 100 square degrees. Now keep in mind that the Sun is half a degree across. The uncertainty in figuring out where the source was consisted of a box the area of which was the equivalent of 500 of our Suns! The error box included parts of constellations Scorpio and Norma, and it touched the border of the constellation Ara. So clearly they were unable to determine in which constellation the source was located.
1963年4月，赫伯特·弗里德曼在华盛顿特区海军研究实验室的研究小组对该辐射源的位置进行了大幅改进。他们发现它位于天蝎座。因此，该辐射源现在被称为Sco X-1。X代表“X射线”，1表示它是第一个在天蝎座发现的X射线源。尽管从未被提及，但它具有重要的历史意义。天蝎座 X-1 的位置与 Giacconi 等人论文中给出的误差框中心大约相差 25 度，该论文标志着 X 射线天文学的诞生。当天文学家在天鹅座发现新的 X 射线源时，它们被命名为天鹅座 X-1（简称 Cyg X-1）、天鹅座 X-2 等等；在武仙座发现的第一个 X 射线源是 Her X-1；在半人马座发现的第一个 X 射线源是 Cen X-1。在接下来的三年里，人们利用火箭发现了大约十几个新的 X 射线源，但除了一个重要的例外——位于金牛座的 Tau X-1 之外，没有人知道它们是什么，也不知道它们是如何产生如此巨大的 X 射线，以至于我们可以在数千光年之外探测到它们。
In April 1963 Herbert Friedman’s group at the Naval Research Laboratory in Washington, D.C. improved substantially on the source’s position. They found that it was located in the constellation Scorpio. That’s why the source is now known as Sco X-1. The X stands for “X-rays,” and the 1 indicates that it was the first X-ray source discovered in the constellation Scorpio. It is of historical interest, though never mentioned, that the position of Sco X-1 is about 25 degrees away from the center of the error box given in the Giacconi et al. paper that marked the birth of X-ray astronomy. When astronomers discovered new sources in the constellation Cygnus (the Swan), they received the names Cygnus X-1 (or Cyg X-1 for short), Cyg X-2, and so on; the first source discovered in the constellation Hercules was Her X-1; in Centaurus Cen X-1. Over the next three years about a dozen new sources were discovered using rockets, but with one important exception, namely Tau X-1, located in the constellation Taurus, no one had any idea what they were, or how they were producing X-rays in such huge quantities that we could detect them thousands of light-years away.
例外情况是天空中一个较为罕见的天体：蟹状星云。如果您不了解蟹状星云，不妨翻到图片插页看看它现在的样子——我猜您一眼就能认出来。网上也有很多它的照片。这是一个距离地球约6000光年的非凡天体——它是公元1054年一次超新星爆发的惊人遗迹，被中国天文学家记录下来（很可能也被美洲原住民的象形文字所记录——请看这里：http ://seds.org/messier/more/m001_sn.html#collins1999 ），当时它被描述为一颗突然出现在金牛座的超亮星体，仿佛凭空出现一般。（关于确切日期存在一些争议，但许多人认为是7月4日。）当月，它是除月亮外天空中最亮的天体；甚至在白天也能看到它，持续了好几个星期；而且在接下来的两年里，晚上也还能看到它。
The exception was one of the more unusual objects in the sky: the Crab Nebula. If you don’t know about the Crab Nebula, it’s worth turning to the photo insert to look at the image of it there now—I suspect you’ll recognize it right away. There are also many photos of it on the web. It’s a truly remarkable object about 6,000 light-years away—the stunning remains of a supernova explosion in the year 1054 recorded by Chinese astronomers (and quite possibly in native American pictographs—take a look here: http://seds.org/messier/more/m001_sn.html#collins1999) as a superbright star in the heavens that suddenly appeared, more or less out of nowhere, in the constellation Taurus. (There is some disagreement about the exact date, though many claim July 4.) That month it was the brightest object in the sky other than the Moon; it was even visible during the day for several weeks, and you could still see it at night for another two years.
然而，当它逐渐消失后，科学家们似乎将其遗忘，直到18世纪，两位天文学家约翰·贝维斯和查尔斯·梅西耶分别独立地发现了它。此时，超新星的残骸（称为超新星遗迹）已经变成了星云状天体。梅西耶编制了一份重要的天文目录，其中包含彗星、星云和星团等天体——蟹状星云是他目录中的第一个天体，编号为M-1。1939年，来自利克的尼古拉斯·梅奥尔发现了蟹状星云。（位于北加州的）天文台确定 M-1 是 1054 年超新星爆发的残骸。如今，在爆炸发生一千年后，蟹状星云内部仍然发生着如此奇妙的事情，以至于一些天文学家毕生致力于研究它。
Once it faded, however, scientists apparently forgot about it until the eighteenth century, when two astronomers, John Bevis and Charles Messier, found it independently of each other. By this time, the remains of the supernova (called a supernova remnant) had become a nebular (cloudlike) object. Messier developed an important astronomical catalog of objects like comets, nebulae, and star clusters—the Crab Nebula is the first object in his catalog, M-1. In 1939 Nicholas Mayall from Lick Observatory (in Northern California) figured out that M-1 is the remnant of the supernova of 1054. Today, a thousand years after the explosion, there is still such wonderful stuff going on inside the Crab Nebula that some astronomers devote entire careers to studying it.
赫伯·弗里德曼的研究小组意识到，1964年7月7日，月球将从蟹状星云正前方经过，遮挡住它的视线。天文学家将这种遮挡现象称为“掩星”——也就是说，月球将掩食蟹状星云。弗里德曼不仅想证实蟹状星云确实是X射线源，他还希望能够证明一些其他的东西——一些更重要的东西。
Herb Friedman’s group realized that the Moon was going to pass right in front of the Crab Nebula on July 7, 1964, and block it from view. The term astronomers use for this blocking out is “occultation”—that is, the Moon was going to occult the Crab Nebula. Not only did Friedman want to confirm that the Crab Nebula was indeed an X-ray source, but he also was hoping he could demonstrate something else—something even more important.
到了1964年，天文学家们对一种早在20世纪30年代就被提出但从未被探测到的天体——中子星——重新燃起了兴趣。这些奇特的天体（我在第12章会有更详细的讨论）被认为是恒星生命最后阶段的产物之一，可能诞生于超新星爆发，主要由中子构成。如果它们真的存在，那么它们的密度将非常高，一颗质量与太阳相当的中子星直径也只有大约10公里——如果你能想象的话，大约是12英里。1934年（中子被发现两年后），沃尔特·巴德和弗里茨·兹威基创造了“超新星”一词，并提出中子星可能形成于超新星爆发中。弗里德曼认为蟹状星云中的X射线源可能就是这样一颗中子星。如果他的说法正确，那么当月球运行到它前面时，他所观测到的 X 射线辐射就会突然消失。
By 1964 a renewed interest had emerged among astronomers in a type of stellar object whose existence was first postulated during the 1930s but that had never been detected: neutron stars. These strange objects, which I discuss more fully in chapter 12, had been conjectured to be one of the final stages in a star’s life, possibly born during a supernova explosion and composed mostly of neutrons. If they existed, they would be of such great density that a neutron star with the mass of our Sun would only be about 10 kilometers in diameter—about 12 miles all the way across, if you can imagine such a thing. In 1934 (two years after the discovery of neutrons), Walter Baade and Fritz Zwicky had coined the term “supernova” and proposed that neutron stars might be formed in supernova explosions. Friedman thought that the X-ray source in the Crab Nebula might be just such a neutron star. If he was right, the X-ray emission he was seeing would disappear abruptly when the Moon passed in front of it.
他决定在月球运行到蟹状星云前方时，连续发射一系列火箭。由于他们知道月球在天空中的确切位置，并且可以将探测器指向该方向，因此他们可以“观测”到蟹状星云消失时X射线强度的下降。结果，他们的探测器确实探测到了X射线强度的下降，而这一观测是首次确凿的光学识别。X射线源的识别。这是一个重大成果，因为一旦我们完成了光学识别，我们就乐观地认为很快就能发现这些神秘而强大的X射线源背后的机制。
He decided to fly a series of rockets, one after the other, right as the Moon was going in front of the Crab Nebula. Since they knew the Moon’s exact position in the sky as it moved, and could point the counters in that direction, they could “watch” for a decline in X-rays as the Crab Nebula disappeared. As it happened, their detectors did indeed pick up a decline, and this observation was the first conclusive optical identification of an X-ray source. This was a major result, since once we had made an optical identification, we were optimistic that we would soon discover the mechanism behind these enigmatic and powerful X-ray sources.
然而，弗里德曼却失望了。X射线并没有像他预想的那样在月球掠过蟹状星云时“消失”，而是逐渐消失，这表明它们来自整个星云，而非某个小型天体。因此，他并没有找到中子星。不过，蟹状星云中确实存在一颗非常特殊的中子星，它确实会发射X射线；这颗中子星的自转速度约为每秒30次！如果你想真正欣赏一番，可以访问钱德拉X射线天文台的网站（http://chandra.harvard.edu/），浏览蟹状星云的图像。我保证，它们绝对令人叹为观止。但45年前，我们还没有轨道成像X射线望远镜，所以我们必须发挥更大的创造力。 （继乔斯林·贝尔于 1967 年发现射电脉冲星之后，弗里德曼的研究小组于 1968 年终于探测到蟹状星云中中子星发出的 X 射线脉冲——大约每秒 30 次。）
Friedman, however, was disappointed. Instead of “winking out” as the Moon passed over the Crab Nebula, the X-rays disappeared gradually, indicating that they came from the nebula as a whole and not from a single small object. So he hadn’t found a neutron star. However, there is a very special neutron star in the Crab Nebula, and it does emit X-rays; the neutron star rotates about its axis about thirty times per second! If you want a real treat, go to the Chandra X-Ray Observatory website (http://chandra.harvard.edu/) and call up images of the Crab Nebula. I promise you, they are stunning. But forty-five years ago we had no orbiting imaging X-ray telescopes in space, so we had to be much more inventive. (After the 1967 discovery of radio pulsars by Jocelyn Bell, in 1968 Friedman’s group finally detected X-ray pulsations—about thirty per second—from the neutron star in the Crab Nebula.)
就在弗里德曼观测蟹状星云掩星现象的同时，我的朋友（未来的）乔治·克拉克当时在麻省理工学院，正在德克萨斯州准备乘坐高空气球进行夜间飞行，以寻找天蝎座X-1的高能X射线。但当他听到弗里德曼的观测结果时——即使没有互联网，消息传播得也很快——他彻底改变了计划，改为白天飞行，寻找来自蟹状星云的能量超过15千电子伏特的X射线。而且他也找到了！
Just as Friedman was observing the occultation of the Crab, my friend (to be) George Clark at MIT was in Texas preparing for a high-altitude balloon night flight to search for high-energy X-rays from Sco X-1. But when he heard about Friedman’s results—even without the Internet, news traveled fast—he completely changed his plans and switched to a day flight in search of X-rays in excess of about 15 keV from the Crab Nebula. And he found them too!
这一切令人无比激动，难以用语言形容。我们正处于科学探索新时代的黎明。我们感觉自己揭开了遮蔽宇宙奇妙领域的帷幕。事实上，通过将探测器送入如此高的地方，进入太空，到达大气层顶部——X射线可以穿透大气层而不被空气吸收——我们移除了人类历史上一直蒙蔽我们双眼的“滤镜”。我们进入了一个全新的光谱领域。
It’s hard to put into words just how exciting all this was. We were at the dawn of a new era in scientific exploration. We felt we were lifting a curtain that had been hiding these amazing realms of the universe. In reality, by getting our detectors up so high, by getting into space, by getting to the top of the atmosphere where X-rays could penetrate without being absorbed by air, we were removing blinding filters that had been on our eyes for all of human history. We were operating in a whole new spectral domain.
这种情况在天文学史上屡见不鲜。每次我们发现天体发出新的或不同类型的辐射时，都会发生这种情况。由于辐射的发现，我们不得不改变我们对恒星、它们的生命周期（它们的诞生、生存以及死亡的方式和原因）、星团的形成和演化、星系，甚至星系团的认知。例如，射电天文学向我们展示了星系中心可以喷射出长达数十万光年的喷流；它还发现了脉冲星、类星体和射电星系，并发现了宇宙微波背景辐射，这彻底改变了我们对早期宇宙的认识。伽马射线天文学发现了宇宙中最强大（也最遥远）的一些爆炸，即伽马射线暴，它们会发出X射线、可见光乃至无线电波的余辉。
That has happened often in the history of astronomy. Every time we learned that objects in the heavens emitted new or different kinds of radiation, we had to change what we thought we knew about stars, about their life cycles (how they are born, how they live, and how and why they die), about the formation and evolution of clusters of stars, about galaxies, and even about clusters of galaxies. Radio astronomy, for instance, showed us that the centers of galaxies can emit jets hundreds of thousands of light-years long; it has also discovered pulsars, quasars, and radio galaxies and is responsible for the discovery of cosmic microwave background radiation, which radically changed our views of the early universe. Gamma-ray astronomy has discovered some of the most powerful and (fortunately) distant explosions in the universe, known as gamma-ray bursts, which emit afterglows in X-rays and visible light all the way down to radio waves.
我们知道，太空X射线的发现将会改变我们对宇宙的认知。只是我们当时并不知道具体会如何改变。有了新设备，我们无论看向哪里，都能看到新的事物。这或许并不令人惊讶。当光学天文学家开始从哈勃太空望远镜获取图像时，他们激动不已，惊叹万分，而且——也许这一点并不那么明显——他们渴望了解更多。但他们本质上只是在扩展一台有着数百年历史的仪器的探测范围，而这个领域本身的历史可以追溯到数千年前。作为X射线天文学家，我们正在见证一个全新科学领域的黎明。谁又能预知它将引领我们走向何方，或者我们将发现什么呢？我们当然不知道！
We knew that the discovery of X-rays in space was going to change our understanding of the universe. We just didn’t know how. Everywhere we looked with our new equipment, we saw new things. That’s not surprising, perhaps. When optical astronomers started getting images from the Hubble Space Telescope, they were thrilled, awestruck, and—maybe this isn’t so obvious—hungry for more. But they were basically extending the reach of a centuries-old instrument, in a field dating back millennia. As X-ray astronomers, we were experiencing the dawn of a whole new scientific field. Who knew where it would lead, or what we would discover? We surely didn’t!
1966年1月，布鲁诺·罗西邀请我去麻省理工学院，当时这个领域正蓬勃发展，我真是太幸运了。我立刻加入了乔治·克拉克的研究小组。乔治是一位非常非常聪明的物理学家，一个令人印象深刻的人，我们成了终生挚友。直到现在，我仍然难以置信自己如此幸运——一个月内既收获了一位挚友，又开启了新的职业生涯。
How fortunate for me that Bruno Rossi invited me to MIT in January 1966, just as this field was taking off, and that I immediately joined George Clark’s group. George was a very, very smart physicist, a really impressive guy with whom I became friends for the rest of my life. Even now, I can hardly believe my good luck—a great friend and a new career, both in the same month.
第十一章
CHAPTER 11
X射线气球探测的早期阶段
X-ray Ballooning, the Early Days
我刚到麻省理工学院时，世界上只有五个活跃的气球观测小组：麻省理工学院的乔治·克拉克（George Clark）、澳大利亚阿德莱德大学的肯·麦克拉肯（Ken McCracken）、麻省理工学院的吉姆·奥弗贝克（Jim Overbeck）、加州大学圣地亚哥分校的拉里·彼得森（Larry Peterson）以及莱斯大学的鲍勃·海姆斯（Bob Haymes）。本章主要讲述我本人参与X射线气球观测的经历，这项技术是我1966年至1976年这十年间研究的核心。在此期间，我曾在德克萨斯州帕勒斯坦、亚利桑那州佩吉、加拿大卡尔加里以及澳大利亚等地进行观测。
When I arrived at MIT, there were five active balloon groups in the world: George Clark at MIT, Ken McCracken at the University of Adelaide in Australia, Jim Overbeck at MIT, Larry Peterson at UC San Diego, and Bob Haymes at Rice University. This chapter is largely about my own experiences with X-ray ballooning, which was at the center of my research in the decade between 1966 and 1976. During these years I made observations from Palestine, Texas; Page, Arizona; Calgary, Canada; and Australia.
我们的气球将X射线探测器带到了约145,000英尺（约30英里）的高空，那里的大气压只有海平面的0.3%。在如此稀薄的大气中，能量高于15千电子伏特的X射线有相当一部分能够穿透大气层。
Our balloons carried our X-ray detectors to an altitude of about 145,000 feet (about 30 miles), where the atmospheric pressure is only 0.3 percent of that at sea level. When the atmosphere is this thin, a good fraction of X-rays with energies above 15 keV get through.
我们的气球观测是对火箭观测的补充。火箭搭载的探测器通常观测能量范围在1到10千电子伏特之间的X射线，而且在整个飞行过程中观测时间仅约五分钟。而气球观测可以持续数小时（我最长的飞行时间是26小时），我的探测器观测到的能量范围在15千电子伏特以上的X射线。
Our balloon observations complemented the rocket observations. Rocket-borne detectors typically observed X-rays in the range from 1 to 10 keV and only for about five minutes during an entire flight. Balloon observations could last for hours (my longest flight was twenty-six hours) and my detectors observed X-rays in the range above 15 keV.
并非所有在火箭观测期间探测到的信号源都是由于这些辐射源通常以低能X射线的形式释放大部分能量，因此我们能够利用气球观测探测到它们。另一方面，我们也能够探测到主要发射高能X射线的辐射源，而这些辐射源在火箭观测中是不可见的。因此，我们不仅发现了新的辐射源，并将已知辐射源的光谱扩展到了高能范围，而且还能够探测到辐射源X射线亮度在几分钟到几小时时间尺度上的变化，这是火箭观测无法实现的。这是我早期天体物理研究的一项重要成果。
Not all sources that were detected during rocket observations were detectable during balloon observations, since the sources often emitted most of their energy at low-energy X-rays. On the other hand, we were able to detect sources emitting largely high-energy X-rays invisible during rocket observations. Thus, not only did we discover new sources and extend the spectra of known sources to high energies, but we also were capable of detecting variability in the X-ray luminosity of sources on time scales of minutes to hours, which was not possible with rockets. This was one of the early successes of my research in astrophysics.
1967年，我们发现了天蝎座X-1的一次X射线耀斑——这真是个惊人的发现——稍后我会在本章详细介绍。我的团队还发现了三个X射线源：GX 301-2、GX 304-1和GX 1+4，它们在之前的火箭观测中从未被观测到过，而且它们的X射线强度都在几分钟内发生变化。GX 1+4甚至还表现出周期性变化，周期约为2.3分钟。当时我们完全不知道是什么原因导致了如此快速的X射线强度变化，更不用说2.3分钟的周期性了，但我们知道我们正在开辟新的领域——揭开新的面纱。
In 1967 we discovered an X-ray flare from Sco X-1—that was a real shocker—I’ll tell you all about this later in this chapter. My group also discovered three X-ray sources, GX 301-2, GX 304-1, and GX 1+4, never seen before during rocket observations, and all of them showed changes in their X-ray intensity on time scales of minutes. GX 1+4 even showed periodic variability with a period of about 2.3 minutes. At the time we had no idea what could be the cause of such rapid changes in the X-ray intensity, let alone the 2.3-minute periodicity, but we knew we were breaking new ground—uncovering new territory.
然而，即使到了20世纪60年代末，一些天文学家仍然没有意识到X射线天文学的重要性。1968年，我在布鲁诺·罗西的家中见到了荷兰天文学家扬·奥尔特。奥尔特是当时最著名的天文学家之一，他是一位极具远见的先驱；二战结束后，他立即在荷兰启动了一项完整的射电天文学计划。那一年他来到麻省理工学院时，我给他看了我们1966年和1967年气球飞行的数据。但他却对我说——我永远都会记得这句话——“X射线天文学并不重要。” 你敢相信吗？“并不重要。” 他大错特错了。这位可是史上最伟大的天文学家之一，却对X射线天文学的重要性视而不见。也许是因为当时我更年轻、更有干劲——公平地说，他当时已经六十八岁了——我清楚地意识到我们正在收获纯金，而我们仅仅触及了皮毛。
For some astronomers, though, even in the late 1960s, the significance of X-ray astronomy hadn’t yet sunk in. In 1968, I met the Dutch astronomer Jan Oort at Bruno Rossi’s home. Oort was one of the most famous astronomers. He had been an incredible visionary; right after World War II, he started a whole radio astronomy program in the Netherlands. When he came to MIT that year, I showed him the balloon data from our flights in 1966 and 1967. But he said to me—and I’ll always remember this—“X-ray astronomy is just not very important.” Can you believe it? “Just not very important.” He couldn’t have been more wrong. This was one of the greatest astronomers of all time, and he was completely blind to its significance. Maybe because I was younger, and hungrier—to be fair, he was sixty-eight by then—it was obvious to me that we were harvesting pure gold, and we were only just scratching the surface.
我记得在20世纪60年代和70年代，我会阅读每一篇关于X射线天文学的论文。1974年，我在莱顿做了五场讲座。（奥尔特当时就在我的听众席上），所以我得以涵盖X射线天文学的方方面面。如今，每年都有成千上万篇关于X射线天文学的论文发表，涉及众多子领域，没有人能够完全掌握整个领域。许多研究人员毕生致力于数十个特定主题之一，例如单星、吸积盘、X射线双星、球状星团、白矮星、中子星、黑洞、超新星遗迹、X射线暴、X射线喷流、星系核和星系团。早年是我最美好的时光。那段日子也充满挑战，几乎方方面面都如此：智力上的、体力上的，甚至后勤保障上的。发射气球既复杂又昂贵，耗时费力，而且令人紧张，我简直难以形容。不过，我会尽力描述。
I remember in the 1960s and 1970s I would read every single paper that came out on X-ray astronomy. In 1974 I gave five lectures in Leiden (Oort was in my audience), and I was able to cover all of X-ray astronomy. Nowadays thousands of papers on X-ray astronomy are published every year, in a multitude of subfields, and no one can grasp the entire field. Many researchers spend their entire careers on one of dozens of specific topics such as single stars, accretion disks, X-ray binaries, globular clusters, white dwarfs, neutron stars, black holes, supernovae remnants, X-ray bursts, X-ray jets, galactic nuclei, and clusters of galaxies. The early years were the most fantastic years for me. They were also demanding, in just about every way: intellectually, physically, even logistically. Launching balloons was so complicated and expensive, time-consuming, and tension producing, I can hardly describe it. I’ll try, though.
升空：气球、X射线探测器和发射
Getting Aloft: Balloons, X-ray Detectors, and the Launch
在物理学家开展任何工作之前（除非你是理论物理学家，他们可能只需要一张纸或一台电脑屏幕），你必须先筹集资金来购置设备、支付学生工资，有时甚至需要长途跋涉。科学家们的大部分工作实际上是在竞争激烈的项目中撰写科研经费申请书，以获得研究经费支持。我知道这听起来既不吸引人也不浪漫，但相信我，没有这些，什么都做不成。真的，什么都做不成。
Before a physicist can do anything (unless, that is, you’re a theorist, who may need only a piece of paper or a computer screen), you have to get the money to build equipment and pay students and sometimes to travel very far. Lots of what scientists really do is write grant proposals, in highly competitive programs, to get supported to do research. I know it’s not sexy or romantic, but believe me, nothing happens without it. Nothing.
你可能有一个绝妙的实验或观察想法，但如果你不知道如何将其转化为一份成功的提案，那就毫无意义。我们一直都在与世界上最优秀的人竞争，所以竞争非常残酷。对于几乎所有领域的科学家来说，情况依然如此。无论你观察一位成功的实验科学家——生物学、化学、物理学、计算机科学、经济学还是天文学，都一样——你看到的都是那些一次又一次战胜竞争对手的人。这通常意味着他们性格并不和善。这就是为什么我的妻子苏珊在麻省理工学院工作了十年，她常说：“麻省理工学院里没有小人物。”
You could have a wonderful idea for an experiment or an observation, and if you don’t know how to transform it into a winning proposal, it goes nowhere. We were always competing against the best in the world, so it was a cutthroat business. It still is, for just about any scientist in any field. Whenever you look at a successful experimental scientist—in biology, chemistry, physics, computer science, economics, or astronomy, it doesn’t matter—you are also looking at someone who’s figured out how to beat the competition over and over again. That does not make for warm and fuzzy personalities, for the most part. It’s why my wife, Susan, who’s worked at MIT for ten years, is fond of saying, “There are no small egos at MIT.”
假设我们获得了资助，而我们通常都能获得资助（我得到了美国国家科学基金会和NASA的慷慨支持）。要将一个携带2000磅重X射线望远镜（连接着降落伞）的气球送上近30英里的高空，并且还要确保它完好无损地回收，这绝对是一个非常复杂的过程。发射时必须有稳定平静的天气，因为气球非常脆弱，一阵风就可能让整个任务功亏一篑。还需要一些基础设施——发射场、运载火箭等等——来帮助气球升入高空并进行追踪。由于我想观测银河系中心（我们称之为银河系中心）的大致方向，那里有很多X射线源，所以我需要从南半球进行观测。我选择了从澳大利亚的米尔杜拉和爱丽丝泉发射。那时我已经有了四个孩子，离家和家人非常远，通常要离开几个月。
Suppose we got the funding, which we usually did (I was generously supported by the National Science Foundation and NASA). To send a balloon up nearly 30 miles, carrying a 2,000-pound X-ray telescope (connected to a parachute), which you had to recover intact, was a very complex process. You had to have reliably calm weather at launch, because the balloons were so delicate that a gust of wind could sink the whole mission. You needed to have some infrastructure—launch sites, launch vehicles, and the like—to help get the balloons way up into the atmosphere and to track them. Since I wanted to observe in the general direction of the center of the Milky Way, which we call the galactic center, where many X-ray sources were located, I needed to observe from the Southern Hemisphere. I chose to launch from Mildura and Alice Springs, Australia. I was very far away from my home and family—I had four children by then—usually for a couple of months at a time.
发射气球的一切都耗资不菲。气球本身就非常巨大。我发射过的最大的一个（当时是史上最大的气球，现在可能仍然是）体积高达5200万立方英尺；完全充气后，在14.5万英尺的高空飞行时，直径约为235英尺。这些气球由非常轻的聚乙烯制成——厚度只有千分之二英寸，比保鲜膜或香烟纸还薄。如果在发射过程中触地，它们就会撕裂。这些巨大而美丽的气球重约700磅。我们通常会带一个备用气球，每个气球的成本高达10万美元——在40年前，这可是一笔巨款。
Everything about the launches was expensive. The balloons themselves were enormous. The largest one I flew (which at the time was the largest balloon ever flown, and it may well still be the largest ever) had a volume of 52 million cubic feet; when fully inflated and flying at 145,000 feet, its diameter was about 235 feet. The balloons were made of very lightweight polyethylene—one-half of one-thousandth of an inch thick, thinner than Saran Wrap or cigarette paper. If they ever touched the ground during launch, they would tear. These gigantic, beautiful balloons weighed about 700 pounds. We usually traveled with a backup, and each one cost $100,000—forty years ago, when that was real money.
它们必须在巨型工厂里生产。气球的各个部分，也就是看起来像橘子皮的扇形片，都是单独制作，然后用热封工艺拼接起来的。制造商只信任女性进行热封工作；他们说，众所周知，男性太没耐心，而且容易出错。之后，我们还得把氦气从遥远的澳大利亚运过来给气球充气。光是氦气，每个气球就要花费大约8万美元。按现在的美元计算，仅仅一个气球加上氦气就要超过70万美元，这还不包括备用气球、交通、住宿和餐饮。没错——我们当时就是这么穷。我住在澳大利亚沙漠腹地，过着与世隔绝的生活，努力探寻深空的秘密，完全依赖天气。而且我还没跟你提杰克呢。我一会儿再说杰克。
They had to be made in immense plants. The gores, the sections of the balloon that look like tangerine skin segments, were made separately and then put together by heat sealing. The manufacturer only trusted women to do the sealing; they said it was well known that men were too impatient and made too many mistakes. Then we had to ship the helium to inflate the balloons all the way to Australia. The helium alone cost about $80,000 per balloon. In current dollars that was more than $700,000 for just one balloon and its helium, without even considering the backup balloon, our transportation, lodging, or food. That’s right—here we were trying to ferret out the secrets of deep space, living in the middle of the Australian desert, utterly dependent on the weather. And I haven’t even told you about Jack. I’ll get to Jack in a bit.
但与望远镜相比，气球的成本微乎其微。每台望远镜都是极其复杂的机器，重约一吨，建造大约需要两年时间，耗资100万美元——相当于今天的400万美元。我们从来没有足够的资金同时建造两台望远镜。所以，如果我们丢失了望远镜——这种情况发生过两次——至少两年内我们都将束手无策。在获得资金之前，我们甚至无法开始建造新的望远镜。因此，丢失一台望远镜对任何人来说都是一场灾难。
But the balloons were cheap compared to the telescopes. Each telescope, an extremely complicated machine weighing about a ton, took roughly two years to build and cost $1 million—$4 million in today’s dollars. We never had enough money for two telescopes at a time. So if we lost our telescope—which happened twice—we were out of luck for at least two years. We couldn’t even start building a new one until we’d gotten the funding. So it was a catastrophe if we lost one.
而且这不仅仅影响到我，远不止如此。这会严重耽误我的研究生们的进度，他们都深度参与了望远镜的建造，他们的博士论文也都是关于仪器和观测结果的。他们的学位会随着气球一起飘向远方。
And not just for me, not at all. This would cause a major delay for my graduate students, who were all deeply involved in building the telescopes, and whose PhD theses were about the instruments and the results of the observations. Their degrees went up in the air with the balloons.
我们也需要天气的配合。平流层中存在着强劲的风，一年中大约有六个月的时间，风速自东向西，大约每小时100英里；而剩下的半年则自西向东。每年两次，这些风会改变方向——我们称之为“风向反转”——在风向反转期间，145,000英尺高空的风速会变得非常低，这使我们能够进行数小时的观测。因此，我们需要找到一个能够测量这些风速，并且能够在风向反转期间发射探测器的地方。我们每隔一天就用探空气球进行探测，并用雷达追踪它们。大多数情况下，这些探空气球在升到大约125,000英尺（约24英里）高空后就会爆裂。但是，预测大气层并非像在实验室演示中推动滚珠轴承那样简单。大气层要复杂得多，也更难以预测，然而我们所做的一切都依赖于做出准确的预测。
We needed the cooperation of the weather, too. There are intense winds in the stratosphere, flowing east to west at about 100 miles per hour for about six months of the year, and west to east the other half of the year. Twice a year these winds reverse direction—we call it the turnaround—and as they do, the wind speeds at 145,000 feet become very low, which would allow us to make observations for many hours. So we needed to be in a place where we could measure these winds and could launch during the turnaround. We probed every other day with weather balloons that we tracked by radar. Most of the time they would make it to about 125,000 feet, about 24 miles up, before they popped. But predicting the atmosphere isn’t like pushing ball bearings down a track in a lab demonstration. The atmosphere is so much more complex, so much less predictable, and yet everything we did depended on making good forecasts.
还有更多。在大约3万到6万英尺的高度，大气层被称为对流层顶，那里非常非常冷——零下50摄氏度（零下58华氏度）——我们的气球会变得非常脆弱。那里还有喷射气流，它们会猛烈地拍打气球。然后它就可能爆裂。太多事情都可能出错。我的气球曾经被吹到海里——望远镜也就此报废。有效载荷九个月后在新西兰的海滩上被找到。奇迹般地，在柯达公司的帮助下，我们得以恢复记录在机载胶片上的数据。
There was more. At an altitude between about 30,000 and 60,000 feet the atmosphere is called the tropopause, where it’s very, very cold—minus 50 degrees Celsius (–58°F)—and our balloons would get very brittle. There were jet stream winds too, and they beat on the balloon, which could then burst. So many things could go wrong. Once my balloon blew out to sea—end of telescope. The payload was found nine months later on a beach in New Zealand. Miraculously, with the help of Kodak, we were able to retrieve the data, which were recorded on film on board.
为了这些发射，我们一遍又一遍地做准备，但我总是说，即便我们做了万全的准备，仍然需要一点运气。有时，甚至需要很多运气。我们会把设备运到这个偏远的站点。然后，我们会对望远镜进行测试，校准仪器，确保一切运转正常。我们会检查连接望远镜和降落伞的索具，降落伞最终也会连接到气球上。在气球发射场完成所有测试并做好飞行准备可能需要大约三周时间，但之后天气可能并不配合。那时我们除了坐在那里等待、给电池充电之外，别无他法。幸好爱丽丝泉非常美丽：这座迷人的沙漠小镇位于澳大利亚的中心地带。它真的感觉像是在荒郊野外，但天空晴朗，我们尝试发射的清晨景色壮丽：黎明前的夜空呈现出深邃的蓝色，随着太阳升起，天空和沙漠被染成了绚丽的粉色和橙色。
We prepared over and over and over for these launches, and yet I always said that even though we prepared like crazy, we still needed a little luck. Sometimes a lot of luck. We would bring the equipment to this remote station. Then we did tests on the telescope, calibrating the instruments and making sure everything was working. We would go through the rigging connecting the telescope to the parachute, which would eventually connect to the balloon as well. It could take us about three weeks to do all the tests at the balloon launching site and be flight ready, and then the weather might not cooperate. And we had nothing else to do then except to sit there and wait and keep the batteries charged. It’s a good thing Alice Springs was so beautiful: a fantastic desert town right in the heart of Australia. It really felt like it was in the middle of nowhere, but the skies were clear and the early mornings when we tried to launch were spectacular: the night sky had turned its predawn deep blue, and as the Sun rose it painted the sky and the desert in brilliant pinks and oranges.
准备就绪后，我们需要风速低于每小时3英里且风向稳定三到四个小时，因为气球升空需要这么长时间（光充气就需要两个小时）。所以我们大多选择在黎明时分升空，那时风力最小。但天气预报也可能不准，那样我们就只能一直等待，直到天气配合为止。
Once we were ready to go, we needed to have winds under 3 miles per hour in a steady direction for three or four hours, which is how long it took to get the balloon off the ground (the inflation alone took two hours). That’s why we mostly launched at dawn, when there was the least amount of wind. But it could happen that our forecast was wrong, and we just had to wait, and wait, and wait some more, until the weather cooperated.
有一次在米尔杜拉，我们正准备发射望远镜——甚至还没开始充气——突然刮起了风，完全出乎气象员的意料。气球被吹灭了，谢天谢地，望远镜安然无恙！所有的准备工作，还有20万美元——瞬间化为乌有。真是太可惜了。我们只能等待天气好转，然后用备用气球再试一次。
We were in the middle of a launch one time in Mildura—we had not even started inflation—and the wind came up, contrary to the weatherman’s forecast. The balloon was destroyed, but thank goodness the telescope was safe! All that preparation, and $200,000—gone in a few seconds. Talk about painful. All we could do was wait for better weather and try again with our spare balloon.
失败的阴影挥之不去。上次去爱丽丝泉的探险，我们连续损失了两个气球，都是在发射时发生的，因为发射人员犯了一些致命的错误。我们的探险彻底失败了——但至少我们的望远镜没有受损。它甚至都没能升空。还有一次（1980年），在德克萨斯州的巴勒斯坦，八小时的飞行很成功，但当我们通过无线电指令终止飞行时，我们的望远镜却丢失了；降落伞根本没打开。
The failures stick with you. On my last expedition to Alice Springs we lost two balloons in a row right at launch, because the launch crew made some tragic mistakes. Our expedition was a complete failure—but at least our telescope wasn’t damaged. It never left the ground. On my last expedition (in 1980), in Palestine, Texas, the eight-hour flight was successful, but when we terminated the flight by radio command, we lost our telescope; the parachute never opened.
即使在今天，气球发射也远非万无一失。2010年4月，美国宇航局（NASA）在爱丽丝泉的一次气球发射尝试中出现故障，气球在起飞过程中坠毁，造成价值数百万美元的设备损毁，并险些伤及围观者。您可以在这里查看相关报道：www.physorg.com/news191742850.html
Even today, balloon launches are far from a sure thing. In an attempted NASA launch from Alice Springs in April 2010, something went wrong and the balloon crashed while trying to take off, destroying millions of dollars worth of equipment and nearly injuring onlookers. You can see the story here: www.physorg.com/news191742850.html.
这些年来，我大概放飞过二十个气球。只有五个在发射过程中失败或没能升到预定高度（可能是氦气泄漏）。这算是相当不错的成功率（75%）。插图中可以看到气球充气（充氦气）和气球发射的照片。
Over the years I must have launched about twenty balloons. I had only five that failed during launch or didn’t get to altitude (they may have been leaking helium). That was considered a good success rate (75 percent). In the insert you can see a picture of the inflation (with helium) of a balloon and also a picture of a balloon launch.
在前往发射场前几个月，我们会在马萨诸塞州威尔明顿的一家公司对有效载荷进行测试。我们将望远镜放入真空室，并将气压降至与高空相同的水平，大约千分之三大气压。然后，我们将其冷却至零下50摄氏度（零下58华氏度），并启动所有X射线探测器，每隔20分钟监测10秒钟来自放射源的X射线，持续24小时。我们的一些竞争对手的望远镜——是的，我们确实认为其他做类似研究的团队是我们的竞争对手——有时会因为电池在低温下电量下降或完全失效而出现故障。这种情况从未发生在我们身上，因为我们进行了非常彻底的测试。如果在测试期间发现电池电量即将下降，我们会想办法在必要时加热电池，以维持其供电。
Months before going to the launch site, we would test the payload at a firm in Wilmington, Massachusetts. We put the telescope into a vacuum chamber and brought the air pressure down to the same we’d have way up high, about three-thousandths of an atmosphere. Then we cooled it down to minus 50 degrees Celsius (–58°F) and ran it—turning on all the X-ray detectors and monitoring for ten seconds every twenty minutes X-rays from a radioactive source for twenty-four hours straight. Some of our competitors’ telescopes—yes, we did feel like the other teams doing the same kinds of things were our competition—would fail sometimes because their batteries would lose power at low temperatures or quit altogether. That never happened to us because we had tested them so thoroughly. If we saw in the testing period that our batteries were going to lose power, we figured out how to heat them up if necessary and keep the power going.
再比如电晕放电的问题——高压电线产生的火花。我们的一些设备采用高压运行，而且电线非常细。空气中气压极低，是火花产生的理想环境，电线放电到空气中就很容易产生火花。还记得我在第七章提到的输电线路周围的嗡嗡声吗？那就是电晕放电。每个从事高压实验的物理学家都知道电晕放电的存在。我在课堂上会展示这些火花的例子。在高空，电晕放电很有趣。但在145,000英尺（约43,000米）的高空，它却是一场灾难。
Or take the problem of corona discharge—sparking from high-voltage wires. Some of our equipment ran on high voltage, and very thin air, where the pressure is very low, is an ideal environment for sparks, from wires into the open air. Remember the buzz around transmission lines I mentioned back in chapter 7? That’s corona discharge. Every experimental physicist who works with high voltage knows you can get corona discharge. I show examples of these sparks in my classes. There, corona discharge is fun. At 145,000 feet, it’s a catastrophe.
通俗地说，设备会开始发出嘶嘶声，产生大量的电子噪声，以至于无法分辨X射线光子。这会造成多大的灾难？彻底的灾难：飞行过程中将无法获得任何可用数据。解决方案是用硅橡胶包裹所有高压电线。其他人也做了同样的事情，但仍然出现了电晕放电。我们的测试和准备工作得到了回报。我们从未遇到过电晕放电。这只是建造这些精密望远镜所涉及的数十个复杂工程问题之一——这就是为什么它们建造起来如此耗时，造价如此高昂的原因。
In lay terms, the equipment would start to sputter, and you would get so much electronic noise that you couldn’t pick out the X-ray photons. How big a disaster would this be? Total and complete: you would get no usable data at all on a flight. The solution was to coat all of our high-voltage wires in silicon rubber. Other folks did the same thing and still got corona discharge. Our testing and preparation paid off. We never had corona discharge. This was just one of dozens of complex engineering issues involved in building these intricate telescopes—that’s why they took so long to build, and cost so much money.
那么，当我们把望远镜送入大气层高处后，我们是如何探测到X射线的呢？这个问题的答案并不简单，请耐心听我解释。首先，我们使用了一种特殊的探测器（碘化钠晶体），而不是火箭使用的那种充满气体的比例计数器，而是能够探测能量高于15 keV的X射线。当X射线光子穿透这些晶体时，它会将一个电子从其轨道上击出，并将X射线能量传递给该电子（这被称为光电吸收）。这个电子在停止运动之前，会在晶体中留下离子轨迹。当这些离子被中和时，它们会释放能量，主要以可见光的形式释放；因此会产生闪光——X射线光子的能量转化为闪光。X射线的能量越高，闪光就越强。我们使用光电倍增管来检测光闪并将其转换为电脉冲：光闪越亮，脉冲电压越高。
So, once we got the telescope high up into the atmosphere, how did we detect X-rays? The answer to this question is not simple, so please bear with me. To begin with, we used a special kind of detector (sodium iodide crystals), not the proportional counters (filled with gas) the rockets used, but something that was able to detect X-rays with energies higher than 15 keV. When an X-ray photon penetrates one of these crystals it can kick an electron out of its orbit and transfer its X-ray energy to that electron (this is called photoelectric absorption). This electron in turn will produce a track of ions in the crystal before it comes to a stop. When these ions get neutralized, they release energy mostly in the form of visible light; thus a flash of light is produced—the energy of the X-ray photon is converted into a light flash. The higher the energy of the X-rays, the stronger the light flashes. We used photomultipliers to detect the light flashes and convert them into electric pulses: the brighter the light flash, the higher the voltage of a pulse.
然后我们放大这些脉冲，并将它们发送到鉴别器，鉴别器测量电脉冲的电压并根据其幅度进行排序——这指示了能量水平。X射线。早期我们只记录了五个不同能量级别的X射线。
We then amplified these pulses and sent them to a discriminator, which measured the voltage of the electric pulses and sorted them according to magnitude—which indicated the energy levels of the X-rays. In the early days we recorded the X-rays at only five different energy levels.
为了在气球飞行后保留探测结果的记录，早期我们在气球上按能量等级和探测时间对探测结果进行了记录。我们将鉴别器连接到发光二极管，使其向这些分类后的脉冲发送信号，从而在五个不同的能量等级下产生闪烁的图案。然后，我们用一台连续胶片相机拍摄了这些闪烁的灯光。
So that we would have a record of the detections after the balloon flight, in the early days we recorded them on board, by energy level and the time they were detected. We wired the discriminator to send these sorted impulses to light-emitting diodes, which created a pattern of flashing lights at those five distinct energy levels. Then we photographed those flashing lights with a camera running continuous film.
如果灯亮着，就会在胶片上留下痕迹。总而言之，一次观测的胶片看起来就像一系列的短划线和直线，短划线和直线。回到麻省理工学院后，我们会用乔治·克拉克设计的一种特殊读取器“读取”胶片，这种读取器可以将这些短划线转换成穿孔纸带：一种带孔的纸带。然后，我们用光敏二极管读取穿孔纸带，并将数据记录到磁带上。我们用Fortran语言（我知道这听起来很原始）在计算机卡上编写了一个程序，并用它将磁带上的数据读入计算机内存，最终——我们终于得到了五个不同能量通道中X射线计数随时间变化的数据。
If a light was on, it would make a track on the film. All together, the film of an observation would look like a series of dashes and lines, lines and dashes. Back at MIT we would “read” the film with a special reader designed by George Clark that converted the lines and dashes to punch tape: paper tape with holes in it. Then we read the punch tape with light sensitive diodes and recorded the data on magnetic tape. We had written a program on computer cards in Fortran (I realize this sounds prehistoric) and used it to read the magnetic tape into the memory of the computer, which—finally!—gave us X-ray counts as a function of time in the five different energy channels.
我知道这听起来像个鲁布·戈德堡机械。但想想我们当时想做什么。我们试图测量X射线光子的计数率（每秒X射线的数量）和能量水平，以及发射它们的源的位置——这些光子以光速传播了数千年，在银河系中扩散，并随着传播距离的平方不断衰减。与稳定的山顶光学望远镜不同，后者的控制系统可以使望远镜连续数小时对准同一位置，并能夜复一夜地返回同一位置，而我们只能利用有限的时间（最多一年一次）——总是以小时计算——让一个脆弱的气球将我们重达一千公斤的望远镜带到地球上方145000英尺（约445000米）的高空。
I know it sounds like a Rube Goldberg machine. But think about what we were trying to do. We were trying to measure the counting rate (the number of X-rays per second) and energy levels of X-ray photons, as well as the location of the source that had emitted them—photons that had been traveling for thousands of years at the speed of light, spreading through the galaxy and thinning out continuously by the square of the distance they traveled. And unlike a stable mountaintop optical telescope whose control system can keep the telescope trained on the same spot for many hours and can return to the same spot night after night, we had to make use of whatever time we had (at most once per year)—always measured in hours—while a fragile balloon carried our thousand-kilo telescope 145,000 feet above the Earth.
当热气球升空时，我驾驶一架小型飞机跟随它，通常都能保持视线范围内（当然是在白天，晚上不行），飞行高度只有5000到10000英尺。你可以想象那是什么感觉，持续好几个小时。一次要飞八、十、十二个小时。我个子也不小。在这些小小的四座飞机上，很容易晕机，真的太容易了。而且，气球升空的时候我一直都很紧张。只有在恢复之后，拿到数据之后，才能真正放松下来。
When a balloon was in flight I followed it in a small plane, usually keeping it in sight (in the daytime, that is—not at night), flying at just 5,000 or 10,000 feet. You can imagine what that was like, for many hours at a time. I’m not a small man. It was easy, all too easy, to get sick in these little four-seater planes, flying for eight, ten, twelve hours at a time. Plus, I was nervous the whole time the balloon was up. The only time you could relax was after the recovery, when you had the data in hand.
这个气球非常巨大，即使升空近30英里，阳光照射时也能清晰可见。借助雷达，我们可以从发射站追踪它很远的距离，直到地球曲率导致追踪失效。因此，我们给气球配备了无线电发射器，到了晚上，我们只能完全依靠无线电信标来追踪它。无论我们如何努力在当地报纸上刊登发射报道，气球还是会漂移数百英里，而当它们升空时，我们就会收到各种各样的不明飞行物报告。这听起来很滑稽，但仔细想想又完全合情合理。当人们瞥见天空中一个大小和距离都无法确定的神秘物体时，他们还能怎么想呢？对他们来说，那确实是一个不明飞行物。插图中可以看到一张用望远镜拍摄的145000英尺高空气球照片。
The balloon was so enormous that even though it was nearly 30 miles up, when sunlight hit it, you could see it very clearly. With radar, we could follow it a long way from the launching station until the curvature of the Earth would make that impossible. That’s why we outfitted the balloon with a radio transmitter, and at night we had to switch exclusively to tracking the balloon by radio beacon. No matter how hard we worked getting articles in the local newspapers about the launch, the balloons could drift hundreds of miles, and when they were aloft we’d get all kinds of reports of UFOs. It was funny, but it made perfect sense, really. What else were people supposed to think when they caught a glimpse of a mysterious entity in the sky of indeterminate size and distance? To them it really was an unidentified flying object. You can see a picture taken with a telescope of a balloon at 145,000 feet in the insert.
即使我们做了周密的计划，参考了天气预报，甚至采取了应对措施，145,000英尺高空的风向仍然难以预测。有一次在澳大利亚，我们原本预计气球会从爱丽丝泉向北飞行，但它却径直向南飞去。我们目视追踪它直到日落，并整夜保持无线电联系。到了早上，它已经非常接近墨尔本，而我们被禁止进入悉尼和墨尔本之间的空域。虽然没有人会把它击落，但我们必须采取行动。因此，当偏离航线的气球即将进入禁飞区时，我们很不情愿地发出了无线电指令，切断了有效载荷。将望远镜与气球分离会导致气球破碎——它无法承受有效载荷突然释放产生的冲击波——望远镜会开始下落，降落伞会打开（1980年除外），然后缓缓飘落，最终将望远镜安全带回地球。气球的大部分碎片也会坠落到地面，通常会散落在一英亩或更大的范围内。这种情况迟早都会发生在每个气球上。每次飞行结束，都是令人伤感的时刻（尽管这是必要的），因为我们要终止任务——切断数据流。我们希望望远镜尽可能长时间地留在空中。那时候我们对数据无比渴望——这才是关键所在。
Even with all our planning, and weather forecasts, and even in turnaround, the winds at 145,000 feet altitude could turn out to be unreliable. Once, in Australia, we had expected the balloon to head north from Alice Springs, but instead it took off straight south. We followed it visually until sunset and kept radio contact with it through the night. By morning it was getting too close to Melbourne, and we were not allowed to enter the air space between Sydney and Melbourne. No one was going to shoot it down, but we had to do something. So when our wayward balloon was just about to reach forbidden air space, we reluctantly gave the radio command that cut the payload loose. Separating the telescope from the balloon would shatter the balloon—it could not survive the shock wave caused by the sudden release of the payload—and the telescope would start to fall, the parachute would open (except in 1980) and slowly float down, bringing the telescope safely back to Earth. Huge pieces of the balloon would also hit the ground, usually spread out over an acre or more. This occurred sooner or later in every balloon flight, and it was always a sad moment (even though it was always necessary), because we were terminating the mission—cutting off the data flow. We wanted the telescope to be aloft as long as possible. We were so hungry for data in those days—that was the whole point.
内陆地区的康复：袋鼠杰克
Recovery in the Outback: Kangaroo Jack
我们在望远镜底部垫上了纸板缓冲垫，以减轻着陆时的冲击力。如果是在白天，而且我们能目视看到气球（当我们发出减速指令时，气球会突然消失），我们很快就能发现降落伞；我们会尽力驾驶小飞机一路追踪降落伞，直到它完全降落。降落伞着陆后，我们会尽可能精确地在一张非常详细的地图上标记出它的位置。
We put cardboard crash pads on the bottom of the telescope to soften its landing. If it was during the day, and we had visual contact with the balloon (which would suddenly disappear when we sent the cut-down command), we would soon spot the parachute; we did our best to follow it all the way down, circling it in our little airplane. Once it landed we would mark its location on a very detailed map as accurately as possible.
接下来才是真正离奇的部分：我们当时身处飞机上，而我们的有效载荷——所有数据，多年心血的结晶——就躺在地上，几乎触手可及，但我们却不能直接降落在沙漠中央去取！我们必须引起当地居民的注意，而我们通常的做法是让飞机低空飞过民宅。沙漠里的房屋相距甚远。居民们都知道低空飞行的飞机意味着什么，通常会走出家门，挥手示意。然后我们会降落在沙漠中最近的简易机场（注意，这里指的是简易飞机，而不是真正的机场），等待他们前来。
Then the really bizarre part started: because here we were, in an airplane, and our payload, with all our data, the culmination of years of work, was lying on the ground, almost within reach, but we couldn’t just land in the middle of the desert and get it! What we had to do was to draw the attention of local people, and the way we usually did this was by flying a plane low over a house. Houses were pretty far apart in the desert. Residents knew what the low-flying plane meant and usually came out of the house and made contact by waving. Then we would land at the nearest airstrip (not to be confused with an airport) in the desert and wait for them to show up.
有一次飞行途中，那片区域房屋稀少，我们不得不四处寻找。最终，我们找到了一个叫杰克的家伙，他住在离最近的邻居50英里远的沙漠里。他酗酒成性，而且精神不太正常。当然，我们一开始并不知道。但我们从空中联系上了他，然后飞到简易机场等候；大约15个小时后，他开着他的卡车出现了，那是一辆破旧的吉普车，没有挡风玻璃，驾驶室只有个顶棚，后面是一个敞开的货舱。杰克喜欢以每小时60英里的速度在沙漠里横冲直撞，追逐并射杀袋鼠。
During one flight, there were so few houses in the area that we had to hunt for a while. Eventually we found this guy Jack living in the desert 50 miles away from his nearest neighbor. He was drunk and pretty crazy. We didn’t know that at first, of course. But we made contact from the air and then flew to the airstrip and waited; after about 15 hours he showed up with his truck, a battered old jeep-like thing with no windshield, just a roof on its cab, and an open bay in back. Jack liked to tear around the desert at 60 miles an hour, chasing and shooting kangaroos.
我留在杰克、卡车和我的一位研究生身边，我们的跟踪飞机则引导我们找到有效载荷。卡车需要穿越未知的区域。我们一直与飞机保持无线电联系。杰克真是帮了我们大忙。他以前经常猎袋鼠，对哪里能开车非常熟悉。
I stayed with Jack and the truck and one of my graduate students, while our tracking airplane directed us to the payload. The truck needed to go across unmarked terrain. We kept in radio contact with the plane. We were lucky with Jack. From all that kangaroo hunting he really knew where he could drive.
他还有个我讨厌的糟糕游戏，但我们当时已经很依赖他了，所以我也没办法；他只给我演示过一次。他把狗放在吉普车顶上，加速到每小时60英里，然后猛踩刹车，狗像弹弓一样飞到地上。可怜的狗！杰克哈哈大笑，然后抛出了他的笑点：“老狗学不了新把戏。”
He also had this awful game I hated, but we were already depending on him, so there wasn’t much I could do; he gave me a demonstration just once. He put his dog on the roof of the jeep, accelerated up to 60 miles an hour, then slammed on the brakes, and the dog catapulted through the air onto the ground. The poor dog! Jack laughed and laughed and then delivered his punch line: “You can’t teach an old dog new tricks.”
我们花了半天时间才到达目的地，那里有一只六英尺长的鬣蜥守卫着——那家伙看起来真够吓人的。说实话，它把我吓得魂飞魄散。但我当然不想表现出来，所以我对我的研究生说：“没问题。这些动物无害。你先去。” 他照做了，结果证明它们确实无害。在我们花了整整四个小时才把货物运到杰克的卡车上的过程中，这只鬣蜥一动不动。
It took us half a day to reach the payload, which was being guarded by a six-foot-long iguana—a really nasty-looking creature. To tell the truth, it scared the hell out of me. But of course I didn’t want to show that, so I said to my graduate student, “There’s no problem. These animals are harmless. You go first.” And he did, and it turns out that they are harmless, and during the entire four hours it took us to recover the payload and get it on Jack’s truck, this animal never moved.
气球教授
The Balloon Professor
然后我们回到了爱丽丝泉，不出所料，《中部倡导者报》的头版刊登了一张热气球升空的精彩照片。标题是“太空探索启动” ，文章讲述了“热气球教授”的回归。我成了当地小有名气的人物，在扶轮社和高中给学生们做演讲，甚至还在一家牛排馆做过一次，这让我赢得了请全组人员吃饭的报酬。我们真正想做的是尽快把胶卷带回家，冲洗并分析，看看我们有什么发现。所以，经过几天的清理工作后，我们就出发了。你可以想象这种研究有多么耗费精力。我至少每隔一年（有时甚至每年）就要离家两个月左右。毫无疑问，我的第一次婚姻因此受到了很大的影响。
Then we went back to Alice Springs, and of course we were on the front page of the Centralian Advocate with a great photograph of the balloon launch. The headline read START OF SPACE PROBE and the article talked about the “balloon professor” having returned. I had become a sort of local celebrity and gave talks to the Rotary Club and for students at the high school, even once in a steak house, which earned me dinner for my crew. What we really wanted to do was take our film back home as quickly as possible, develop and analyze it, and see what we’d found. So after a few days’ cleanup we were on our way. You can see just how demanding this kind of research was. I was away from home for something like two months at least every other year (sometimes every year). And there’s no question about it that my first marriage suffered a lot because of it.
与此同时，尽管气氛紧张焦虑，但这段经历既令人兴奋又充满乐趣，我为我的研究生们感到骄傲，尤其是杰夫·麦克林托克和乔治·里克。杰夫现在是哈佛-史密森天体物理中心的高级天体物理学家，并因其测量X射线双星系统中黑洞质量的工作而荣获2009年罗西奖（你猜是谁的名字？）。（我们将在第13章详细介绍。）我很高兴地告诉大家，乔治仍然在麻省理工学院工作。他非常擅长设计和开发创新型仪器。他最著名的研究领域是伽马射线暴。
At the same time, despite all the nervousness and tension, it was exciting and great fun and I was proud of my graduate students, notably Jeff McClintock and George Ricker. Jeff is now senior astrophysicist at the Harvard-Smithsonian Center for Astrophysics and won the 2009 Rossi Prize (named for guess who?) for his work measuring the masses of black holes in X-ray binary star systems. (We’ll get to that in chapter 13.) George, I’m happy to say, still works at MIT. He is brilliant at designing and developing innovative new instrumentation. He is best known for his research in gamma-ray bursts.
热气球之旅别有一番浪漫情调。凌晨四点起床，驱车前往机场，欣赏日出，见证热气球壮观的充气过程——在这片美丽的沙漠上，头顶是繁星点点的夜空，然后太阳缓缓升起。接着，热气球缓缓升空，在晨曦中闪耀着银金色的光芒。你知道有多少细节必须完美无缺，所以全程都紧张得手心冒汗。天哪！如果一切顺利，所有可能引发灾难的细节都一一到位——那感觉真是妙不可言！
Ballooning was very romantic in its way. To be up at four o’clock in the morning, drive out to the airport, and see the sunrise and see the spectacular inflation of the balloon—this beautiful desert, under the sky, just stars at first, and then slowly seeing the Sun come up. Then, as the balloon was released and pulled itself into the sky, it shimmered silver and gold in the dawn. And you knew just how many little things had to go just right, so all your nerves were jangling the entire time. My goodness. And if it seemed to be a good launch, in which the myriad details (each one of which was the source of a potential disaster) seemed to fall into place one after another—what an incredible feeling!
那时候我们确实走在了时代的前沿。想想看，我们的成功竟然部分取决于一位喝醉的澳大利亚袋鼠猎人的慷慨解囊。
We really were on the cutting edge in those days. To think that success partly depended on the generosity of a drunken Australian kangaroo hunter.
来自天蝎座 X-1 的 X 射线耀斑
An X-ray Flare from Sco X-1
那些年里，我们取得的任何发现中最令我兴奋的，莫过于一个完全出乎意料的发现：某些X射线源的X射线辐射量会出现显著的爆发式变化。早在20世纪60年代中期，人们就已开始讨论某些X射线源的强度会发生变化。1964年10月1日，洛克希德导弹与航天公司的菲利普·费舍尔及其团队将他们火箭飞行中探测到的七个X射线源的强度，与弗里德曼团队1964年6月16日火箭飞行中探测到的强度进行了比较。他们发现，天鹅座XR-1源（现称为天鹅座XR-1）的X射线强度（我们称之为X射线通量）发生了显著变化。10月1日的X射线-1值比6月14日低了五倍。但这一观测结果是否真正反映了X射线的变异性尚不清楚。费舍尔的研究小组指出，弗里德曼的研究小组使用的探测器对低能X射线比他们使用的探测器灵敏得多，这或许可以解释两者之间的差异。
No discovery we made in those years was more thrilling for me than the totally unexpected finding that some X-ray sources have remarkable flare-ups in the amount of X-rays they emit. The idea that the X-ray intensity from some sources varies was in the air as early as the mid-1960s. Philip Fisher and his group at Lockheed Missiles and Space Company compared the X-ray intensities of seven X-ray sources detected during their rocket flight on October 1, 1964, with those of a rocket flight by Friedman’s group on June 16, 1964. They found that the X-ray intensity (which we call X-ray flux) for the source Cyg XR-1 (now called Cyg X-1) was five times lower on October 1 than on June 14. But whether or not this observation demonstrated real variability was unclear. Fisher’s group pointed out that the detectors used by Friedman’s group were much more sensitive to low-energy X-rays than the detectors they had used and that this might explain the difference.
这个问题在1967年得到了解决。当时，弗里德曼的研究小组比较了过去两年中30个X射线源的流量，并确定许多X射线源的强度确实存在变化。天鹅座X-1的强度变化尤为引人注目。
The issue was settled in 1967 when Friedman’s group compared the X-ray flux of thirty sources over the prior two years and determined that many sources really did vary in intensity. Particularly striking was the variability of Cyg X-1.
1967年4月，澳大利亚肯·麦克拉肯的研究小组发射了一枚火箭，发现了一个亮度几乎与天蝎座X-1（当时我们所知的最亮的X射线源）相当的天体，而一年半前探测器观测同一地点时却并未发现它。在华盛顿特区举行的美国物理学会春季会议上，这个被称作“X射线新星”的天体被宣布两天后，我与一位X射线天文学领域最杰出的先驱通了电话，他问我：“你相信这种胡说八道吗？”
In April 1967, Ken McCracken’s group in Australia launched a rocket and discovered a source nearly as bright as Sco X-1 (the brightest X-ray source we knew of), which had not shown up when detectors had observed the same spot a year and a half earlier. Two days after the announcement of this “X-ray nova” (as it was called) during the spring meeting of the American Physical Society in Washington D.C., I was on the phone with one of the most eminent pioneers in X-ray astronomy, and he said to me, “Do you believe that nonsense?”
它的强度在几周内下降了三分之二，五个月后，强度至少下降了五十分之一。如今，我们用通俗易懂的名称“X射线瞬变源”来称呼这些天体。
Its intensity went down in a few weeks by a factor of three, and five months later its intensity had diminished by at least a factor of fifty. Nowadays, we call these sources by the pedestrian name “X-ray transients.”
麦克拉肯的团队在南十字座（Crux）找到了辐射源。他们为此感到非常兴奋，这甚至让他们激动不已，因为南十字座正是澳大利亚国旗上的星座。然而，当发现辐射源的实际位置并非南十字座，而是在半人马座时，最初的名称“Crux X-1”被改为“Cen X-2”，澳大利亚人对此感到非常失望。科学家们对自己的发现往往会非常激动。
McCracken’s group had located the source in the constellation Crux, which you may know better as the Southern Cross. They were very excited about this, and it became something of an emotional thing for them, since that very constellation is in the Australian flag. When it turned out that the source’s location was just outside the Southern Cross, in Centaurus instead, the original name Crux X-1 was changed to Cen X-2, and the Aussies were very disappointed. Scientists can get very emotional about our discoveries.
1967年10月15日，我和乔治·克拉克乘坐热气球从澳大利亚米尔杜拉升空，进行了长达十小时的飞行，观测了天蝎座X-1卫星，并取得了一项重大发现。这项发现与你在休斯顿NASA航天中心的照片中看到的截然不同——照片里，人们在取得成功时欢呼雀跃、互相拥抱。他们亲眼见证的是真实发生的奇迹。时间紧迫。观测期间我们无法获取数据；我们只能祈祷气球能坚持到最后，设备也能完美运行。当然，我们始终担心如何才能把望远镜和数据运回来。那真是既紧张又兴奋的时刻。
On October 15, 1967, George Clark and I observed Sco X-1 in a ten-hour balloon flight launched from Mildura, Australia, and we made a major discovery. This discovery wasn’t anything like you see in pictures of the NASA Space Center in Houston, where they all cheer and hug one another when they have a success. They are seeing things happen in real time. During our observing we had no access to the data; we were just hoping that the balloon would last and that our equipment would work flawlessly. And, of course, we always worried about how to get the telescope and the data back. That’s where all the nerves and the excitement were.
几个月后，我们回到麻省理工学院分析了数据。一天晚上，我在机房里，特里·索索斯（Terry Thorsos）在一旁协助我。那时候麻省理工学院的计算机非常庞大。由于计算机运行会产生大量热量，机房必须配备空调。我记得当时大约是晚上十一点。如果想运行一些程序，晚上是偷偷运行的好时机。那时候，运行程序总是需要一名计算机操作员。我排了个队，耐心地等待着。
We analyzed our data months later, back home at MIT. I was in the computer room one night, assisted by Terry Thorsos. We had very large computers at MIT in those days. The rooms had to be air-conditioned because the computers generated so much heat. I remember that it was around eleven p.m. If you wanted to get some computer runs, the evening was a good time to sneak in some jobs. In those days you always needed to have a computer operator to run your programs. I got into a queue and waited patiently.
当时我正在查看气球数据，突然发现天蝎座X-1的X射线通量大幅增加。就在打印输出上，X射线通量在大约十分钟内增加了四倍，持续了近三十分钟，然后逐渐减弱。我们观测到了天蝎座X-1的一次X射线耀斑，而且威力巨大。这种情况以前从未被观测到过。通常情况下，你会想：“这次耀斑会不会有其他解释？会不会是探测器故障造成的？” 但这次我毫不怀疑。我对这台仪器了如指掌。我相信我们所有的准备和测试，在整个飞行过程中，我们持续检查探测器，并且每隔二十分钟就测量一次已知放射源的X射线光谱作为对照——仪器运行完美无瑕。我对数据百分之百信任。查看打印输出，我可以看到X射线通量有起伏变化；在那十个小时的飞行中，我们观察到的所有信号源中，只有一个上下移动，那就是 Sco X-1。它是真的！
So here I was, looking at the balloon data, and all of a sudden I saw a large increase in the X-ray flux from Sco X-1. Right there, on the printout, the X-ray flux went up by a factor of four in about ten minutes, lasted for nearly thirty minutes, and then subsided. We had observed an X-ray flare from Sco X-1, and it was enormous. This had never been observed before. Normally, you’d say to yourself, “Is this flare something that could be explained in a different way? Was it perhaps caused by a malfunctioning detector?” In this case, there was no doubt in my mind. I knew the instrument inside and out. I trusted all our preparation and testing, and throughout the flight we had checked the detector continuously and had measured the X-ray spectrum of a known radioactive source every twenty minutes as a control—the instruments were working flawlessly. I trusted the data 100 percent. Looking at the printout I could see that the X-ray flux went up and down; of all the sources we observed in that ten-hour flight, only one shot up and down, and that was Sco X-1. It was real!
第二天早上，我把结果给乔治·克拉克看，他差点从椅子上摔下来。我们俩对这个领域都很熟悉，真是欣喜若狂！此前没有人预料到，更别说观测到，X射线通量会发生这种变化。在十分钟的时间尺度上，该源的流量变化幅度与Cen X-2相比，在首次探测到该源后的几周内下降了三倍，但我们在这里的流量变化幅度在十分钟内就达到了四倍——速度快了大约三千倍。
The next morning I showed George Clark the results, and he nearly fell off his chair. We both knew the field well; we were overjoyed! No one had anticipated, let alone observed, a change in the flux of an X-ray source on a time scale of ten minutes. The flux from Cen X-2 decreased by a factor of three within a few weeks after the first detection, but here we had variability by a factor of four within ten minutes—about three thousand times faster.
我们知道天蝎座X-1 99.9%的能量都以X射线的形式释放出来，它的X射线亮度大约是太阳总亮度的1万倍，是太阳X射线亮度的100亿倍。天蝎座X-1的亮度在短短十分钟内变化了四倍——这在当时的物理学中根本无法解释。如果我们的太阳在十分钟内亮度增加四倍，你该如何解释？这简直太可怕了。
We knew that Sco X-1 emitted 99.9 percent of its energy in the form of X-rays, and that its X-ray luminosity was about 10,000 times the total luminosity of our Sun and about 10 billion times the X-ray luminosity of the Sun. For Sco X-1 to change its luminosity by a factor of four on a time scale of ten minutes—well, there was simply no physics to understand it. How would you explain it if our Sun would become four times brighter in ten minutes? It would scare the hell out of me.
在这一时间尺度上发现的变率可能是利用气球进行X射线天文学观测的最重要发现。正如我在本章中提到的，我们也发现了火箭无法观测到的X射线源，这些发现同样意义重大。但没有任何其他发现能与天蝎座X-1的十分钟变率相提并论。
The discovery of variability on this time scale may have been the most important discovery in X-ray astronomy made from balloons. As I mentioned in this chapter, we also discovered X-ray sources that the rockets couldn’t see, and those were important discoveries as well. But nothing else had the impact of Sco X-1’s ten-minute variability.
当时这完全出乎意料，许多科学家都难以置信。即使是科学家，也常常抱有根深蒂固的期望，难以动摇。《天体物理学杂志快报》的传奇编辑S·钱德拉塞卡将我们关于Sco X-1的文章送审，而审稿人完全不相信我们的发现。四十多年过去了，我仍然记得这件事。他写道：“这一定是无稽之谈，因为我们知道，这些强大的X射线源不可能在十分钟的时间尺度上发生变化。”
It was so unexpected at the time that many scientists couldn’t believe it. Even scientists have powerful expectations that can be difficult to challenge. The legendary editor of the Astrophysical Journal Letters, S. Chandrasekhar, sent our Sco X-1 article to a referee, and the referee didn’t believe our finding at all. I still remember this, more than forty years later. He wrote, “This must be nonsense, as we know that these powerful X-ray sources cannot vary on a time scale of ten minutes.”
我们不得不费尽口舌才能让论文发表在期刊上。罗西在1962年也经历过同样的事情。《物理评论快报》的编辑塞缪尔·古德斯米特接受了这篇奠定X射线天文学基础的文章，因为罗西就是罗西，而且正如他后来所写的那样，他愿意对论文的内容承担“个人责任”。
We had to talk our way into the journal. Rossi had had to do exactly the same thing back in 1962. The editor of Physical Review Letters, Samuel Goudsmit, accepted the article founding X-ray astronomy because Rossi was Rossi and was willing, as he wrote later, to assume “personal responsibility” for the contents of the paper.
如今，由于我们拥有灵敏度更高的仪器和望远镜，我们知道许多X射线源在任何时间尺度上都会发生变化，这意味着如果你连续每天观测一个X射线源，它的辐射通量每天都会不同。如果你每秒观测一次，情况也会随之改变。即使你逐毫秒分析数据，也可能发现某些数据源存在波动。但当时，这种十分钟的波动是前所未有的。
Nowadays, because we have instruments and telescopes that are so much more sensitive, we know that many X-ray sources vary on any timescale, meaning that if you observe a source continuously day by day, its flux will be different every day. If you observe it second by second it will change as well. Even if you analyze your data millisecond by millisecond you may find variability in some sources. But at the time, the ten-minute variability was new and unexpected.
1968年2月，我在麻省理工学院就这项发现做了演讲，看到里卡多·贾科尼和赫伯·古尔斯基也在听众席中，我激动不已。我感觉自己终于功成名就，被接纳进入了我所在领域的前沿。
I gave a talk about this discovery at MIT in February 1968, and I was thrilled to see Riccardo Giacconi and Herb Gursky in the audience. I felt as though I’d arrived, that I had been accepted into the cutting edge of my field.
接下来的几章里，我将向你们介绍X射线天文学已经解开的一系列谜团，以及我们天体物理学家仍在努力寻找答案的一些谜团。我们将前往中子星，并深入黑洞的深处。准备好迎接惊喜吧！
In the next few chapters I’ll introduce you to the host of mysteries that X-ray astronomy solved, as well as to some we astrophysicists are still struggling to find answers for. We’ll travel to neutron stars and plunge into the depths of black holes. Hold on to your hats.
第十二章
CHAPTER 12
宇宙灾难、中子星和黑洞
Cosmic Catastrophes, Neutron Stars, and Black Holes
中子星是X射线天文学发展史上的核心。而且它们真的非常非常酷。这里说的“酷”并非指温度，而是它们的表面温度经常超过一百万开尔文，比太阳表面温度高出一百多倍。
Neutron stars are smack dab at the center of the history of X-ray astronomy. And they are really, really cool. Not in terms of temperature, not at all: they can frequently have surface temperatures upward of a million kelvin. More than a hundred times hotter than the surface of our Sun.
詹姆斯·查德威克于1932年发现了中子（并因此荣获1935年诺贝尔物理学奖）。在这一非凡的发现之后，许多物理学家认为它完善了原子结构图景。沃尔特·巴德和弗里茨·兹威基随后提出假设：中子星形成于超新星爆发。事实证明，他们的假设完全正确。中子星的诞生源于大质量恒星生命末期发生的剧烈事件——核心坍缩超新星爆发，这是已知宇宙中最迅速、最壮观、最剧烈的事件之一。
James Chadwick discovered the neutron in 1932 (for which he received the Nobel Prize in Physics in 1935). After this extraordinary discovery, which many physicists thought had completed the picture of atomic structure, Walter Baade and Fritz Zwicky hypothesized that neutron stars were formed in supernova explosions. It turns out that they were right on the money. Neutron stars come into being through truly cataclysmic events at the end of a massive star’s lifetime, one of the quickest, most spectacular, and most violent occurrences in the known universe—a core-collapse supernova.
中子星并非起源于像太阳一样的恒星，而是起源于质量至少是太阳八倍的恒星。银河系中可能存在超过十亿颗这样的恒星，但由于银河系中各种类型的恒星数量庞大，即使数量如此之多，这些巨型中子星仍然算是稀有星体。如同我们世界乃至宇宙中的许多天体一样，恒星之所以能够“存在”，是因为它们能够勉强维持各种强大力量之间的平衡。核燃烧恒星的核心会产生巨大的压力，那里发生的热核反应温度高达数千万开尔文，并释放出巨大的能量。我们太阳核心的温度约为1500万开尔文，其能量产生速率相当于每秒超过十亿颗氢弹爆炸的能量。
A neutron star doesn’t begin with a star like our Sun, but rather with a star at least eight times more massive. There are probably more than a billion such stars in our galaxy, but there are so many stars of all kinds in our galaxy that even with so many, these giants must still be considered rare. Like so many objects in our world—and universe—stars can only “live” by virtue of their ability to strike a rough balance between immensely powerful forces. Nuclear-burning stars generate pressure from their cores where thermonuclear reactions at temperatures of tens of millions of degrees kelvin generate huge amounts of energy. The temperature at the core of our own Sun is about 15 million kelvin, and it produces energy at a rate equivalent to more than a billion hydrogen bombs per second.
在一颗稳定的恒星中，这种压力与恒星巨大质量产生的引力基本平衡。如果这两种力——热核反应产生的向外推力和引力产生的向内拉力——不能相互平衡，那么恒星就会不稳定。例如，我们知道太阳已经存在了大约50亿年，并且应该还能继续运行50亿年。当恒星即将死亡时，它们会发生巨大的变化，而且变化方式非常壮观。当恒星耗尽核心的大部分核燃料后，许多恒星在生命的最后阶段会先上演一场绚丽的爆炸。对于大质量恒星来说尤其如此。从某种意义上说，超新星就像戏剧中的悲剧英雄，他们通常会在一次充满宣泄的情感爆发中结束自己漫长的一生，有时是炽热的，常常是震耳欲聋的，正如亚里士多德所说，会唤起观众的怜悯和恐惧。
In a stable star, this pressure is pretty well balanced by the gravity generated by the huge mass of the star. If these two forces—the outward thrust of the thermonuclear furnace and the inward-pulling grip of gravity—didn’t balance each other, then a star wouldn’t be stable. We know our Sun, for example, has already had about 5 billion years of life and should continue on that path for another 5 billion years. When stars are about to die, they really change, and in spectacular ways. When stars have used up most of the nuclear fuel in their cores, many approach the final stages of their lives by first putting on a fiery show. This is especially true for massive stars. In a way, supernovae resemble the tragic heroes of theater, who usually end their overlarge lives in a paroxysm of cathartic emotion, sometimes fiery, often loud, evoking, as Aristotle said, pity and terror in the audience.
所有恒星死亡方式中最惊人的莫过于核心坍缩超新星爆发，这是宇宙中最剧烈的现象之一。我会尽力把它描述清楚。当这些大质量恒星核心的核反应堆开始逐渐停止运转——燃料终究会耗尽！——并且它产生的压力也开始减弱时，剩余质量那永无止境的引力最终会将其彻底摧毁。
The most extravagant stellar demise of all is that of a core-collapse supernova, one of the most energetic phenomena in the universe. I’ll try to do it justice. As the nuclear furnace at the core of one of these massive stars begins to wind down—no fuel can last forever!—and the pressure it generates begins to weaken, the relentless, everlasting gravitational attraction of the remaining mass overwhelms it.
恒星耗尽燃料的过程其实相当复杂，但也十分引人入胜。像大多数恒星一样，质量巨大的恒星最初也是通过燃烧氢并生成氦来维持生命的。恒星的能量来源是核能——不是核裂变，而是核聚变：四个氢原子核（质子）在极高的温度下聚变成一个氦原子核，并产生热量。当这些恒星耗尽氢燃料时，它们的核心会因为引力作用而收缩，从而使温度升高到足以维持生命的程度。它们可以开始将氦聚变成碳。对于质量超过太阳十倍左右的恒星，碳燃烧之后，它们会依次经历氧燃烧、氖燃烧、硅燃烧，最终形成铁核。
This process of exhausting fuel is actually rather complicated, but it’s also fascinating. Like most stars, the really massive ones begin by burning hydrogen and creating helium. Stars are powered by nuclear energy—not fission, but fusion: four hydrogen nuclei (protons) are fused together into a helium nucleus at extremely high temperatures, and this produces heat. When these stars run out of hydrogen, their cores shrink (because of the gravitational pull), which raises the temperature high enough that they can start fusing helium to carbon. For stars with masses more than about ten times the mass of the Sun, after carbon burning they go through oxygen burning, neon burning, silicon burning, and ultimately form an iron core.
每个燃烧周期结束后，恒星核心都会收缩，温度升高，然后下一个周期开始。每个周期产生的能量都比前一个周期少，持续时间也比前一个周期短。举例来说（取决于恒星的确切质量），氢燃烧周期可能持续1000万年，温度约为3500万开尔文；而最后一个周期，硅燃烧周期，可能只持续几天，温度约为30亿开尔文！在每个周期中，恒星都会燃烧掉前一个周期的大部分产物。这简直就是循环利用！
After each burning cycle the core shrinks, its temperature increases, and the next cycle starts. Each cycle produces less energy than the previous cycle and each cycle is shorter than the previous one. As an example (depending on the exact mass of the star), the hydrogen-burning cycle may last 10 million years at a temperature of about 35 million kelvin, but the last cycle, the silicon cycle, may only last a few days at a temperature of about 3 billion kelvin! During each cycle the stars burn most of the products of the previous cycle. Talk about recycling!
当硅聚变生成铁时，能量链就走到了尽头。铁是元素周期表中原子核最稳定的元素。铁聚变成更重的原子核并不产生能量；相反，它需要能量，因此能量产生过程到此结束。随着恒星不断产生铁，铁核迅速增长。
The end of the line comes when silicon fusion produces iron, which has the most stable nucleus of all the elements in the periodic table. Fusion of iron to still heavier nuclei doesn’t produce energy; it requires energy, so the energy-producing furnace stops there. The iron core quickly grows as the star produces more and more iron.
当这个铁核的质量达到约1.4个太阳质量时，它就达到了一个神奇的极限，被称为钱德拉塞卡极限（以伟大的钱德拉·钱德拉·钱德拉·钱德拉的名字命名）。此时，铁核内部的压力再也无法抵抗强大的引力，铁核会自身坍缩，引发向外扩散的超新星爆发。
When this iron core reaches a mass of about 1.4 solar masses, it has reached a magic limit of sorts, known as the Chandrasekhar limit (named after the great Chandra himself). At this point the pressure in the core can no longer hold out against the powerful pressure due to gravity, and the core collapses onto itself, causing an outward supernova explosion.
想象一下，一支庞大的军队围攻一座曾经雄伟的城堡，外墙开始崩塌。（《指环王》电影中的一些战斗场景浮现在脑海，仿佛无穷无尽的兽人军队突破城墙。）城堡核心在几毫秒内坍塌，物质以惊人的速度坠落——实际上，它以接近光速四分之一的速度飞速坠落——将内部温度提升到难以想象的1000亿开尔文，大约是太阳核心温度的一万倍。
Imagine a vast army besieging a once proud castle, and the outer walls begin to crumble. (Some of the battle scenes in the Lord of the Rings movies come to mind, when the apparently limitless armies of Orcs break through the walls.) The core collapses in milliseconds, and the matter falling in—it actually races in at fantastic speeds, nearly a quarter the speed of light—raises the temperature inside to an unimaginable 100 billion kelvin, about ten thousand times hotter than the core of our Sun.
如果一颗恒星的质量小于太阳质量的25倍左右（但大于太阳质量的10倍左右），那么它的坍缩会在其中心形成一种全新的天体：中子星。质量介于太阳质量的 8 倍到 10 倍之间的恒星最终也会变成中子星，但它们核心的核演化（这里不讨论）与上述情况不同。
If a single star is less massive than about twenty-five times the mass of the Sun (but more than about ten times the mass of the Sun), the collapse creates a brand new kind of object at its center: a neutron star. Single stars with a mass between eight and about ten times the mass of the Sun also end up as neutron stars, but their nuclear evolution in the core (not discussed here) differs from the above scenario.
在坍缩核心的高密度区域，电子和质子会合并。单个电子的负电荷抵消了质子的正电荷，它们结合形成中子和中微子。单个原子核不复存在；它们消失在被称为简并中子物质的物质团中。（终于听到一些有趣的名称了！）我喜欢这种反作用力的名称：中子简并压力。如果这颗潜在的中子星的质量超过大约3个太阳质量（当这颗恒星（称为前身星）的质量大于大约25个太阳质量时，就会出现这种情况），那么引力甚至会压倒中子简并压力，你认为接下来会发生什么？猜猜看。
At the high density of the collapsing core, electrons and protons merge. An individual electron’s negative charge cancels out a proton’s positive charge, and they unite to create a neutron and a neutrino. Individual nuclei no longer exist; they have disappeared into a mass of what is known as degenerate neutron matter. (Finally, some juicy names!) I love the name of the countervailing pressure: neutron degeneracy pressure. If this would-be neutron star grows more massive than about 3 solar masses, which is the case if the single star’s mass (called the progenitor) is larger than about twenty-five times the mass of the Sun, then gravity overpowers even the neutron degeneracy pressure, and what do you think will happen then? Take a guess.
没错。我就知道你猜对了。除了黑洞还能是什么呢？黑洞是一个物质无法以任何我们能理解的形式存在的地方；在那里，如果你靠近它，引力会强大到任何辐射都无法逃脱：没有光，没有X射线，没有伽马射线，没有中微子，什么都没有。双星系统的演化（见下一章）可能截然不同，因为在双星系统中，大质量恒星的包层可能在早期就被剥离，核心质量的增长可能不如单星系统那么快。在这种情况下，即使是最初质量是太阳四十倍的恒星，最终也可能演化成一颗中子星。
That’s right. I figured you guessed it. What else could it be but a black hole, a place where matter can no longer exist in any form we can understand; where, if you get close, gravity is so powerful that no radiation can escape: no light, no X-rays, no gamma rays, no neutrinos, no anything. The evolution in binary systems (see the next chapter) can be very different because in a binary the envelope of the massive star may be removed at an early stage, and the core mass may not be able to grow as much as in a single star. In that case even a star that originally was forty times more massive than the Sun may still leave a neutron star.
我想强调的是，形成中子星和黑洞的前身星之间的分界线并不清晰；它取决于许多变量，而不仅仅是前身星的质量；例如，恒星自转也很重要。
I’d like to stress that the dividing line between progenitors that form neutron stars and black holes is not clear cut; it depends on many variables other than just the mass of the progenitor; stellar rotation, for instance, is also important.
但黑洞确实存在——它们并非狂热的科学家和科幻作家的臆想——而且它们极其迷人。它们与X射线宇宙有着千丝万缕的联系，我保证以后会再谈到它们。现在，我只想说：它们不仅真实存在——而且很可能构成了宇宙中所有质量较大的星系的核心。
But black holes do exist—they aren’t the invention of feverish scientists and science fiction writers—and they are incredibly fascinating. They are deeply involved in the X-ray universe, and I’ll come back to them—I promise. For the moment, I’ll just say this: not only are they real—they probably make up the nucleus of every reasonably massive galaxy in the universe.
让我们回到核心坍缩的过程。一旦中子星形成——记住，我们这里讨论的是毫秒级的时间——那些试图冲入其中的恒星物质实际上会被反弹回去，形成向外传播的冲击波。最终，由于剩余铁核的分裂消耗了能量，冲击波会停止传播。（记住，轻元素聚变形成铁核时会释放能量，因此铁核的分裂会消耗能量。）在核心坍缩过程中，当电子和质子融合形成中子时，也会产生中微子。此外，在约1000亿开尔文的高温核心下，还会产生所谓的热中微子。中微子携带了核心坍缩释放的所有能量的约99%（约10⁴⁶焦耳）。剩余的1%（10⁴⁴焦耳）主要以恒星喷射物质的动能形式存在。
Let’s go back to the core collapse. Once the neutron star forms—remember, we’re talking milliseconds here—the stellar matter still trying to race into it literally bounces off, forming an outward-going shock wave, which will eventually stall due to energy being consumed by the breaking apart of the remaining iron nuclei. (Remember that energy is released when light elements fuse to form an iron nucleus, therefore breaking an iron nucleus apart will consume energy.) When electrons and protons merge during core collapse to become neutrons, neutrinos are also produced. In addition, at the high core temperature of about 100 billion kelvin, so-called thermal neutrinos are produced. The neutrinos carry about 99 percent (which is about 1046 joules) of all energy released in the core collapse. The remaining 1 percent (1044 joules) is largely in the form of kinetic energy of the star’s ejected matter.
几乎没有质量且不带电荷的中微子通常能够穿过几乎所有物质，并且大部分都能逃逸出超新星核心。然而，由于周围物质密度极高，它们会将大约1%的能量传递给这些物质，这些物质随后以高达每秒20,000公里的速度被抛射出去。部分抛射物在爆炸后数千年仍能被观测到——我们称之为超新星遗迹（例如蟹状星云）。
The nearly massless and neutral neutrinos ordinarily sail through nearly all matter, and most do escape the core. However, because of the extremely high density of the surrounding matter, they transfer about 1 percent of their energy to the matter, which is then blasted away at speeds up to 20,000 kilometers per second. Some of this matter can be seen for thousands of years after the explosion—we call this a supernova remnant (like the Crab Nebula).
超新星爆发极其耀眼；其最大亮度时的光学光度约为每秒10³⁵焦耳。这相当于太阳亮度的3亿倍，当银河系中发生这样的超新星爆发时（平均每世纪仅发生两次），便会呈现出宇宙中最壮观的景象之一。如今，借助全自动机器人望远镜，每年都能在相对邻近的众多星系中发现数百至上千颗超新星。
The supernova explosion is dazzling; the optical luminosity at maximum brightness is about 1035 joules per second. This is 300 million times the luminosity of our Sun, providing one of the great sights in the heavens when such a supernova occurs in our galaxy (which happens on average only about twice per century). Nowadays, with the use of fully automated robotic telescopes, many hundreds to a thousand supernovae are discovered each year in the large zoo of relatively nearby galaxies.
核心坍缩超新星释放的能量是太阳在过去 50 亿年中产生能量的 200 倍，所有这些能量都在大约 1 秒内释放出来——其中 99% 以中微子的形式释放出来！
A core-collapse supernova emits two hundred times the energy that our Sun has produced in the past 5 billion years, and all that energy is released in roughly 1 second—and 99 percent comes out in neutrinos!
公元1054年，正是这样一件事发生了，那次爆炸产生了过去一千年来天空中最亮的恒星——它如此明亮，以至于在白昼的天空中连续数周都能看到。这是一次真正的宇宙闪光。星际空间中，超新星会在几年内逐渐消失，因为气体冷却并扩散。然而，气体并不会消失。公元1054年的那次爆炸不仅产生了一颗孤立的中子星，还形成了蟹状星云——整个天空中最引人注目且仍在不断变化的各个天体之一，也是新数据、非凡图像和观测发现的几乎无穷无尽的来源。由于许多天文活动发生在极其漫长的时间尺度上，我们通常将其视为地质时间尺度——数百万年甚至数十亿年——因此，当我们发现一些在几秒钟、几分钟甚至几年内发生的快速变化时，就格外令人兴奋。蟹状星云的部分区域每隔几天就会改变形状，哈勃太空望远镜和钱德拉X射线天文台也发现，位于大麦哲伦星云中的1987A超新星残骸也在以我们可观测的方式改变形状。
That’s what happened in the year 1054, and the explosion produced the brightest star in our heavens in the past thousand years—so bright that it was visible in the daytime sky for weeks. A true cosmic flash in the interstellar pan, the supernova fades within a few years, as the gas cools and disperses. The gas doesn’t disappear, though. That explosion in 1054 not only produced a solitary neutron star; it also produced the Crab Nebula, one of the more remarkable and still-changing objects in the entire sky, and a nearly endless source of new data, extraordinary images, and observational discoveries. Since so much astronomical activity takes place on an immense time scale, one we more often think of as geological—millions and billions of years—it’s especially exciting when we find something that happens really fast, on a scale of seconds or minutes or even years. Parts of the Crab Nebula change shape every few days, and the Hubble Space Telescope and the Chandra X-Ray Observatory have found that the remnant of Supernova 1987A (located in the Large Magellanic Cloud) also changes shape in ways we can see.
地球上的三个不同的中微子天文台同时探测到了来自超新星1987A的中微子爆发，其光芒于1987年2月23日抵达地球。中微子极其难以探测，这三个仪器在短短13秒内总共只探测到了25个中微子，而在这13秒内，大约有300万亿（3 × 10¹⁴ ）个中微子倾泻而下，落在地球表面正对超新星的每一平方米上。超新星最初喷射出的中微子数量约为10⁵⁸个，这是一个几乎难以想象的庞大数字——但考虑到它距离地球遥远（约17万光年），最终到达地球的“只有”大约4 × 10²⁸个中微子——比最初喷射出的中微子数量少了30个数量级。超过99.9999999%的中微子直接穿过了地球表面。需要一光年（约 10¹³公里）的铅才能阻止大约一半的中微子。
Three different neutrino observatories on Earth picked up simultaneous neutrino bursts from Supernova 1987A, the light from which reached us on February 23, 1987. Neutrinos are so hard to detect that between them, these three instruments detected a total of just twenty-five in thirteen seconds, out of the roughly 300 trillion (3 × 1014) neutrinos showering down in those thirteen seconds on every square meter of the Earth’s surface directly facing the supernova. The supernova originally ejected something on the order of 1058 neutrinos, an almost unimaginably high number—but given its large distance from the Earth (about 170,000 light-years), “only” about 4 × 1028 neutrinos—thirty orders of magnitude fewer—actually reached the Earth. More than 99.9999999 percent go straight through the Earth; it would take a light-year (about 1013 kilometers) of lead to stop about half the neutrinos.
超新星1987A的前身星大约在两万年前抛射出一层气体壳，这层气体壳在其周围形成了环状结构。这些环状结构在超新星爆发后约8个月才显现出来。抛射气体的速度相对较慢，仅约8公里/秒，但经过多年的演化，这层气体壳的半径已达到约三分之二光年，也就是大约8光月。
The progenitor of Supernova 1987A had thrown off a shell of gas about twenty thousand years earlier that had made rings around the star, and the rings remained invisible until about 8 months after the supernova explosion. The speed of the expelled gas was relatively slow—only around 8 kilometers per second—but over the years the shell’s radius had reached a distance of about two-thirds of a light-year, about 8 light-months.
于是超新星爆发了，大约八个月后，紫外线爆炸产生的光（当然是以光速传播的）追上了物质环，并将其“激活”——于是这个环开始发出可见光。您可以在插图中看到SN 1987A的图片。
So the supernova went off, and about eight months later ultraviolet light from the explosion (traveling at the speed of light, of course) caught up with the ring of matter and turned it on, so to speak—and the ring started to emit visible light. You can see a picture of SN 1987A in the insert.
但还有更多，这还涉及到X射线。超新星爆发时喷射出的气体速度约为每秒2万公里，仅比光速慢约15倍。由于我们当时已经知道星环的距离，因此我们也能大致预测喷射出的物质何时会撞击星环。大约11年后，物质撞击星环，产生了X射线。当然，我们必须始终记住，尽管我们谈论这件事时仿佛它发生在近几十年，但实际上，由于SN 1987A位于大麦哲伦星云中，这一切发生在约17万年前。
But there’s more, and it involves X-rays. The gas expelled by the supernova in the explosion traveled at roughly 20,000 kilometers per second, only about fifteen times slower than the speed of light. Since we knew how far away the ring was by now, we could also predict when, approximately, the expelled matter was going to hit the ring, which it did a little over eleven years later, producing X-rays. Of course, we always have to remember that even though we talk about it as though it happened in the last few decades, in reality, since SN 1987A is in the Large Magellanic Cloud, it all happened about 170,000 years ago.
迄今为止，在SN 1987A的残骸中尚未探测到中子星。一些天体物理学家认为，在中子星形成初期，核心坍缩过程中形成了黑洞。1990年，我和加州大学圣克鲁兹分校的斯坦·伍斯利打了个赌；他是世界顶尖的超新星专家之一。我们打赌五年内能否找到中子星。我输掉了这场一百美元的赌局。
No neutron star has been detected to date in the remnant of SN 1987A. Some astrophysicists believe that a black hole was formed during core collapse after the initial formation of a neutron star. In 1990 I made a bet with Stan Woosley of the University of California, Santa Cruz; he is one of the world’s experts on supernovae. We made a bet whether or not a neutron star would be found within five years. I lost the hundred-dollar bet.
这些非凡的现象带来的远不止这些。在超新星的超高温熔炉中，更高阶的核聚变将原子核猛烈地结合在一起，形成比铁重得多的元素，这些元素最终会聚集在气体云中，并可能最终坍缩成新的恒星和行星。我们人类和所有动物都是由在恒星中孕育的元素构成的。如果没有这些恒星熔炉，如果没有这些惊人的剧烈爆炸（其中第一次爆炸就是宇宙大爆炸），我们就永远不会拥有元素周期表中如此丰富的元素。因此，或许我们可以把核心坍缩型超新星想象成一场天体森林大火（当然，规模很小），它在烧毁一颗恒星的同时，也为新恒星和行星的诞生创造了条件。
There’s more that these remarkable phenomena produce. In the superhot furnace of the supernova, higher orders of nuclear fusion slam nuclei together to create elements far heavier than iron that end up in gas clouds that may eventually coalesce and collapse into new stars and planets. We humans and all animals are made of elements that were cooked in stars. Without these stellar kilns, and without these stunningly violent explosions, the first of which was the big bang itself, we would never have the richness of elements that you see in the periodic table. So maybe we can think of a core-collapse supernova as resembling a celestial forest fire (a small one, to be sure), that in burning out one star creates the conditions for the birth of new stars and planets.
无论从哪个角度来看，中子星都是极端的天体。它们的直径只有十几英里（比一些绕火星运行的小行星还要小）。中子星（例如木星）的体积比太阳小约十万倍，因此其密度比太阳的平均密度高约3000亿倍（3 × 10¹⁴ ）。一茶匙中子星物质的重量相当于地球上的1亿吨。
By any measure neutron stars are extreme objects. They are only a dozen miles across (smaller than some asteroids orbiting between Mars and Jupiter), about hundred thousand times smaller than the Sun, and thus about 300 billion (3 × 1014) times more dense than the average density of the Sun. A teaspoon of neutron star matter would weigh 100 million tons on Earth.
我喜欢中子星的原因之一是，仅仅是说出或写出它们的名字，就将物理学的两个极端——微小和巨大——联系在一起：它们如此之小，我们永远无法看到它们；而它们的体积如此之大，以至于我们的大脑都难以理解。
One of the things I love about neutron stars is that simply saying or writing their name pulls together the two extremes of physics, the tiny and the immense, things so small we will never see them, in bodies so dense that they strain the capacity of our brains.
中子星会自转，有些中子星的自转速度惊人，尤其是在它们刚形成的时候。为什么呢？原因和花样滑冰运动员张开双臂旋转时，收回双臂旋转速度更快一样。物理学家用角动量守恒来解释这种现象。详细解释角动量有点复杂，但这个概念很容易理解。
Neutron stars rotate, some of them at astonishing rates, especially when they first come into being. Why? For the same reason that an ice skater spinning around with her arms out spins more rapidly when she pulls them in. Physicists describe this by saying that angular momentum is conserved. Explaining angular momentum in detail is a bit complicated, but the idea is simple to grasp.
这和中子星有什么关系呢？原因很简单：宇宙中所有物体都在旋转。因此，坍缩成中子星的那颗恒星原本也在旋转。它在爆炸中抛射了大部分物质，但保留了一到两个太阳质量的物质，这些物质现在集中在一个比坍缩前核心体积小几千倍的天体中。由于角动量守恒，中子星的自转频率因此必须至少提高一百万倍。
What does this have to do with neutron stars? Just this: Every object in the universe rotates. So the star that collapsed into the neutron star was rotating. It threw off most of its matter in the explosion but held on to one or two solar masses, now concentrated in an object a few thousand times smaller than the size of the core before collapse. Because angular momentum is conserved, neutron stars’ rotational frequency therefore has to go up by at least a factor of a million.
乔斯林·贝尔发现的前两颗中子星（见下文）绕其轴自转周期约为1.3秒。蟹状星云中的中子星每秒自转约30次，而迄今为止发现的自转速度最快的中子星每秒自转高达惊人的716次！这意味着该恒星赤道处的速度约为光速的15%！
The first two neutron stars discovered by Jocelyn Bell (see below) rotate about their axes in about 1.3 seconds. The neutron star in the Crab Nebula rotates about 30 times per second, while the fastest one that has been found so far rotates an astonishing 716 times per second! That means that the speed at the star’s equator is about 15 percent of the speed of light!
所有中子星都会自转，而且许多中子星都拥有强大的磁场，这一事实催生了一种重要的恒星现象——脉冲星，即“脉动星”的简称。脉冲星是会从其磁极发射无线电波束的中子星，与地球的磁极一样，脉冲星的磁极明显不同于地理极点——地理极点是恒星自转轴末端的点。脉冲星的无线电波随着恒星自转，光束会扫过天空。对于位于光束路径上的观测者来说，恒星会以规律的间隔脉冲闪烁，而观测者只能短暂地看到光束。天文学家有时称之为灯塔效应，原因显而易见。目前已知的单中子星（不要与双中子星混淆）大约有六颗，它们会在极其宽广的电磁波谱范围内脉冲闪烁，包括无线电波、可见光、X射线和伽马射线。蟹状星云中的脉冲星就是其中之一。
The fact that all neutron stars rotate, and that many have substantial magnetic fields, gives rise to an important stellar phenomenon known as pulsars—short for “pulsating stars.” Pulsars are neutron stars that emit beams of radio waves from their magnetic poles, which are, as in the case of the Earth, noticeably different from the geographic poles—the points at the end of the axis around which the star rotates. The pulsar’s radio beam sweeps across the heavens as the star rotates. To an observer in the path of the beam, the star pulses at regular intervals, with the observer only seeing the beam for a brief moment. Astronomers sometimes call this the lighthouse effect, for obvious reasons. There are half a dozen known single neutron stars, not to be confused with neutron stars in binaries, which pulse over an extremely large range of the electromagnetic spectrum, including radio waves, visible light, X-rays, and gamma rays. The pulsar in the Crab Nebula is one of them.
1967年，当时还是英国剑桥大学研究生的乔斯林·贝尔发现了第一颗脉冲星。起初，她和她的导师安东尼·休伊什并不清楚脉冲的规律性，这些脉冲持续时间仅约0.04秒，间隔约1.3373秒（这被称为脉冲星周期）。他们最初将这颗脉冲星命名为LGM-1，意为“小绿人”，暗示这种规律的脉冲可能是外星生命产生的。不久之后，贝尔又发现了第二颗LGM，其周期约为1.2秒。由此可以确定，这些脉冲并非外星生命所致——为什么两个截然不同的文明会以几乎相同的周期向地球发送信号呢？贝尔和休伊什发表他们的研究成果后不久，康奈尔大学的托马斯·戈尔德就认识到脉冲星是旋转的中子星。
Jocelyn Bell discovered the first pulsar in 1967 when she was a graduate student in Cambridge, England. She and her supervisor, Antony Hewish, at first didn’t know what to make of the regularity of the pulsations, which lasted for only about 0.04 seconds and were about 1.3373 seconds apart (this is called the pulsar period). They initially called the pulsar LGM-1, for “Little Green Men,” hinting that the regular pulsations might have been the product of extraterrestrial life. A second LGM was soon discovered by Bell with a period of about 1.2 seconds, and it became clear that the pulses were not produced by extraterrestrial life—why would two completely different civilizations send signals to Earth with about the same period? Shortly after Bell and Hewish published their results, it was recognized by Thomas Gold at Cornell University that pulsars were rotating neutron stars.
黑洞
Black Holes
我早就说过我们会走到这一步。现在终于到了直面这些奇异天体的时候了。我理解人们为什么会害怕它们——如果你在YouTube上花点时间，就会看到几十个关于黑洞的“模拟”视频，其中大多数都属于“死星”或“吞噬恒星”的范畴。在人们的普遍想象中，黑洞是威力无比的宇宙深渊，注定要将一切吞噬进它们永无止境的巨口。
I told you we’d get here. It is finally time to look directly at these bizarre objects. I understand why people might be afraid of them—if you spend a little time on YouTube, you’ll see dozens of “re-creations” of what black holes might look like, and most of them fall in the category of “death stars” or “star eaters.” In the popular imagination black holes are super-powerful cosmic sinkholes, destined to suck everything into their insatiable maws.
但认为即使是超大质量黑洞也会吞噬其周围的一切，这种说法完全是谬论。各种各样的物体，主要由恒星组成的星系将围绕恒星级黑洞甚至超大质量黑洞稳定运行。否则，我们所在的银河系早就消失在其中心那个质量相当于400万个太阳的巨大黑洞中了。
But the notion that even a supermassive black hole swallows up everything in its vicinity is a complete fallacy. All kinds of objects, chiefly stars, will orbit a stellar mass black hole or even a supermassive black hole with great stability. Otherwise, our own Milky Way would have disappeared into the enormous 4-million-solar-mass black hole at its center.
那么，我们对这些奇特的天体了解多少呢？一颗中子星的质量最多只能达到太阳质量的3倍左右，超过这个数值，它就会在引力作用下坍缩成黑洞。如果最初的单核燃烧恒星的质量超过太阳质量的25倍左右，那么在核心坍缩时，物质会继续坍缩，而不是停留在中子星阶段。结果呢？最终会形成黑洞。
So what do we know about these strange beasts? A neutron star can only contain up to about 3 solar masses before the gravitational pull collapses it to form a black hole. If the original single nuclear-burning star was more massive than about twenty-five times the mass of the Sun, at core collapse the matter would continue to collapse rather than stopping at the neutron star stage. The result? A black hole.
如果黑洞在双星系统中拥有伴星，我们可以测量它们对可见伴星的引力影响，在极少数情况下，我们甚至可以确定它们的质量。（我将在下一章讨论这些系统。）
If black holes have companion stars in binary systems, we can measure their gravitational effect on their visible partners, and in some rare cases we can even determine their masses. (I talk about these systems in the next chapter.)
黑洞没有表面，它有一个天文学家称之为“事件视界”的空间边界，在这个边界上，黑洞的引力极其强大，以至于任何东西，甚至电磁辐射，都无法逃脱其引力场。我知道这听起来可能有点难以理解，所以试着想象黑洞就像一个重球静置于一张橡胶片的中央。它会使橡胶片的中心下陷，对吧？如果你手边没有橡胶片，可以用旧丝袜或旧连裤袜代替。剪出一个尽可能大的正方形，在中间放一块石头。然后从四边提起正方形。你会立刻看到，石头在正方形内形成了一个漏斗状的凹陷，就像龙卷风的龙卷风口一样。你刚刚创造了一个三维版本的四维时空现象。物理学家将这种凹陷称为引力井，因为它模拟了引力对时空的影响。如果你用一块更大的石头替换这块石头，你就会挖出一个更深的井，这表明质量更大的物体会更加扭曲时空。
Instead of a surface, a black hole has what astronomers call an event horizon, the spatial boundary at which the black hole’s gravitational power is so great that nothing, not even electromagnetic radiation, can escape the gravitational field. I realize this doesn’t make much sense, so try to imagine that the black hole is like a heavy ball resting in the middle of a rubber sheet. It causes the center to sag, right? If you don’t have a rubber sheet handy, try using an old stocking, or a pair of discarded pantyhose. Cut out as large a square as you can and put a stone in the middle. Then lift the square from the sides. You see immediately that the stone creates a funnel-like depression resembling a tornado spout. Well, you’ve just created a three-dimensional version of what happens in spacetime in four dimensions. Physicists call the depression a gravity well because it mimics the effect gravity has on spacetime. If you replace the stone with a larger rock, you’ll have made a deeper well, suggesting that a more massive object distorts spacetime even more.
因为我们只能在三维空间中思考，所以我们无法真正想象一颗大质量恒星在四维时空中形成漏斗状结构意味着什么。是阿尔伯特·爱因斯坦教会了我们这一点。不妨这样理解引力：它是时空的弯曲。爱因斯坦将引力转化为几何问题，但并非你在高中学到的那种几何。
Because we can only think in three spatial dimensions, we can’t really visualize what it would mean for a massive star to make a funnel out of four-dimensional spacetime. It was Albert Einstein who taught us to think about gravity in this way, as the curvature of spacetime. Einstein converted gravity into a matter of geometry, though not the geometry you learned in high school.
丝袜实验并不理想——我相信这对你们中的许多人来说是个好消息——原因有很多，但最主要的是，你很难想象一颗弹珠能围绕岩石产生的引力井稳定运行。然而，在真实的宇宙中，许多天体都能围绕着巨大的天体稳定运行数百万年甚至数十亿年。想想我们的月球绕着地球运行，地球绕着太阳运行，太阳和我们银河系中其他一千亿颗恒星也都在围绕着我们运行。
The pantyhose experiment is not ideal—I’m sure that will come as a relief to many of you—for a number of reasons, but the main one is that you can’t really imagine a marble in a stable orbit around a rock-generated gravity well. In real astronomical life, however, many objects achieve stable orbits around massive bodies for many millions, even billions of years. Think of our Moon orbiting the Earth, the Earth orbiting the Sun, and the Sun and another 100 billion stars orbiting in our own galaxy.
另一方面，这个演示确实有助于我们形象地理解黑洞。例如，我们可以看到，物体的质量越大，黑洞的深渊就越深，边缘就越陡峭，因此，物体从黑洞中爬出来所需的能量就越多。即使是从大质量恒星引力中逃逸出来的电磁辐射，其能量也会降低，这意味着它的频率会降低，波长会变长。你已经知道，我们将电磁波谱向低能量端的偏移称为红移。对于致密恒星（质量大且体积小），引力也会引起红移，我们称之为引力红移（不要将其与多普勒频移引起的红移混淆——参见第二章和下一章）。
On the other hand, the demonstration does help us visualize a black hole. We can, for instance, see that the more massive the object, the deeper the well and the steeper the sides, and thus the more energy it takes to climb out of the well. Even electromagnetic radiation escaping from the gravity of a massive star has its energy reduced, which means its frequency decreases and its wavelengths become longer. You already know that we call a shift to the less energetic end of the electromagnetic spectrum a redshift. In the case of a compact star (massive and small), there is a redshift caused by gravity, which we call a gravitational redshift (which should not be confused with redshift due to Doppler shift—see chapter 2 and the next chapter).
要逃离行星或恒星的表面，你需要一个最小速度以确保不会坠落回去。我们称之为逃逸速度，地球的逃逸速度约为每秒11公里（约每小时25,000英里）。因此，所有地球卫星的速度都不能超过每秒11公里。逃逸速度越高，逃逸所需的能量就越高，因为能量取决于逃逸速度和想要逃逸的物体的质量m（所需的动能为1/2 mv² ）。
To escape from the surface of a planet or star, you need a minimum speed to make sure that you never fall back. We call this the escape velocity, which is about 11 kilometers per second (about 25,000 miles per hour) for the Earth. Therefore, all satellites bound to Earth can never have a speed larger than 11 kilometers per second. The higher the escape velocity, the higher the energy needed to escape, since this depends both on the escape velocity and on the mass, m, of the objects that want to escape (the required kinetic energy is 1/2 mv2).
你可以想象，如果引力井变得非常非常深，那么从井底逃逸的速度可能会超过光速。由于这不可能，这意味着……任何物质都无法逃脱那深邃的引力井，就连电磁辐射也不例外。
Perhaps you can imagine that if the gravity well becomes very, very deep, the escape velocity from the bottom of the well could become greater than the speed of light. Since this is not possible, it means that nothing can escape that very deep gravity well, not even electromagnetic radiation.
一位名叫卡尔·史瓦西的物理学家解出了爱因斯坦的广义相对论方程，并计算出一个给定质量的球体，其半径达到多少时，会形成一个深不见底的黑洞，任何物质都无法逃脱。这个半径被称为史瓦西半径，其大小取决于物体的质量。这就是我们所说的事件视界的半径。
A physicist named Karl Schwarzschild solved Einstein’s equations of general relativity and calculated what the radius of a sphere with a given mass would be that would create a well so deep that nothing could escape it—a black hole. That radius is known as the Schwarzschild radius, and its size depends on the mass of the object. This is the radius of what we call the event horizon.
这个方程式本身非常简单，但它只适用于非旋转黑洞，通常被称为史瓦西黑洞。该方程式包含一些众所周知的常数，计算结果为每太阳质量略小于3公里。由此我们可以计算出例如10个太阳质量的黑洞的大小——也就是事件视界的半径——约为30公里。我们也可以计算出质量与地球相当的黑洞的事件视界半径——略小于1厘米——但目前没有证据表明这种黑洞存在。那么，如果将太阳的质量集中到一个直径约6公里的球体中，它会像中子星一样吗？不会——在如此巨大的质量聚集在如此小的球体中所产生的引力作用下，太阳的物质会坍缩成黑洞。
The equation itself is breathtakingly simple, but it is only valid for nonrotating black holes, often referred to as Schwarzschild black holes.* The equation involves well-known constants and the radius works out to just a little bit less than 3 kilometers per solar mass. That’s how we can calculate the size—that is to say, the radius of the event horizon—of a black hole of, for example, 10 solar masses, is about 30 kilometers. We could also calculate the radius of the event horizon of a black hole with the mass of the Earth—it would be a little less than 1 centimeter—but there’s no evidence that such black holes exist. So if the mass of our Sun were concentrated into a sphere about 6 kilometers across, would it be like a neutron star? No—under the gravitational attraction of that much mass packed into such a small sphere, the Sun’s matter would have collapsed into a black hole.
早在爱因斯坦之前，1748年，英国哲学家兼地质学家约翰·米歇尔就证明，有些恒星的引力极其强大，以至于光都无法逃逸。他运用了简单的牛顿力学（现在任何一个大一新生都能在30秒内完成），最终得到了与史瓦西相同的结果：如果一颗恒星的质量是太阳质量的N倍，且半径小于3N公里，那么光就无法逃逸。令人惊奇的是，爱因斯坦的广义相对论竟然也得到了与简单的牛顿力学方法相同的结果。
Long before Einstein, in 1748, the English philosopher and geologist John Michell showed that there could be stars whose gravitational pull is so great that light could not escape. He used simple Newtonian mechanics (any of my freshmen can do this now in thirty seconds) and he ended up with the same result as Schwarzschild: if a star has a mass N times the mass of our Sun, and if its radius is less than 3N kilometers, light cannot escape. It is a remarkable coincidence that Einstein’s theory of general relativity gives the same result as a simple Newtonian approach.
在球形事件视界的中心，存在着物理学家所说的……奇点，一个体积为零、密度无穷大的点，一种奇异的事物，它仅仅代表方程的解，而非我们能够理解的本质。奇点究竟是什么，无人知晓，尽管有人进行过一些想象。目前还没有任何物理学理论能够解释奇点的存在。
At the center of the spherical event horizon lies what physicists call a singularity, a point with zero volume and infinite density, something bizarre that only represents the solution to equations, not anything we can grasp. What a singularity is really like, no one has any idea, despite some fantasizing. There is no physics (yet) that can handle singularities.
在网络上，到处可见黑洞的动画视频，它们大多既美丽又令人恐惧，几乎每一个都无比巨大，暗示着宇宙尺度的毁灭性力量。因此，当记者开始报道位于日内瓦附近的世界最大加速器——欧洲核子研究中心的大型强子对撞机（LHC）可能能够制造出黑洞时，他们成功地在非科学界人士中引发了相当大的担忧，认为这些物理学家是在拿地球的未来做赌注。
All over the web you can see animated videos of black holes, most of them at once beautiful and menacing, but nearly all immense beyond belief, hinting at destruction on a cosmic scale. So when journalists began writing about the possibility that the world’s largest accelerator, CERN’s Large Hadron Collider (LHC), near Geneva, might be able to create a black hole, they managed to stir up a good deal of concern among nonscientists that these physicists were rolling dice with the future of the planet.
但他们真的做到了吗？假设他们意外地制造了一个黑洞——它会开始吞噬地球吗？我们可以很容易地推算出答案。2010年3月30日，大型强子对撞机（LHC）中两束反向质子束碰撞的能量为7太电子伏特（TeV），即7万亿电子伏特，每束质子3.5万亿电子伏特。最终，LHC的科学家们计划达到14 TeV的碰撞能量，远远超过目前任何技术所能达到的水平。质子的质量约为1.6 × 10⁻²⁴克。物理学家通常说，质子的质量m约为10亿电子伏特，即1 GeV。当然，GeV代表的是能量而不是质量，但由于E = mc²（c为光速），E通常被称为“质量”。在马萨诸塞州收费公路上，有这样的标志：“拨打511获取旅行信息”。每次看到它，我都会想到电子，因为电子的质量是 511 keV。
But were they really? Suppose they had accidentally created a black hole—would it have started eating up the Earth? We can figure this out fairly easily. The energy level at which opposing proton beams collided in the LHC on March 30, 2010, was 7 teraelectron volts (TeV), 7 trillion electron volts, 3.5 trillion per beam. Ultimately, the LHC scientists plan to reach collisions of 14 TeV, far beyond anything possible today. The mass of a proton is about 1.6 × 10–24 grams. Physicists often say that the mass, m, of a proton is about 1 billion electron volts, 1 GeV. Of course, GeV is energy and not mass, but since E = mc2 (c being the speed of light), E is often referred to as “the mass.” On the Massachusetts Turnpike there are signs: “Call 511 for Travel Information.” Every time I see one I think about electrons, as an electron’s mass is 511 keV.
假设14 TeV碰撞的所有能量都用于形成黑洞，那么它的质量大约是质子的14000倍，也就是大约2 × 10⁻²⁰克。大量的物理学家和评审委员会评估了大量相关文献，发表了他们的研究结果，并得出结论：根本无需担心。你想知道为什么，对吧？问得好。好吧，下面就来分析一下他们的论证。
Assuming that all the energy of the 14 TeV collision went into creating a black hole, it would have a mass of about 14,000 times that of a proton, or about 2 × 10–20 grams. Boatloads of physicists and review committees evaluated a mountain of literature on the question, published their results, and concluded that there was simply nothing to worry about. You want to know why, right? Fair enough. OK, here’s how the arguments go.
首先，大型强子对撞机（LHC）拥有足够能量来产生这种微小黑洞（称为微型黑洞）的情况取决于……所谓“大额外维度”理论，至少可以说仍处于高度推测阶段。该理论远远超出了任何已被实验证实的范围。因此，即便是产生微型黑洞的可能性，首先也极其渺茫。
First, scenarios in which the LHC would have enough energy to create such tiny black holes (known as micro black holes) depend on the theory of something called large extra dimensions, which remains highly speculative, to say the least. The theory goes well beyond anything that’s been experimentally confirmed. So the likelihood even of creating micro black holes is, to begin with, exceptionally slim.
显然，人们担心这些微型黑洞会成为稳定的“吸积体”——能够聚集物质、将其吸入自身并不断增长的天体——并开始吞噬附近的物质，最终甚至吞噬地球。但如果真有稳定的微型黑洞存在，它们早就应该由能量极高的宇宙射线（宇宙射线确实存在）撞击中子星和白矮星而形成，并在那里安家落户。由于白矮星和中子星在数亿年甚至数十亿年的时间尺度上都显得稳定，因此似乎并没有任何微型黑洞从内部吞噬它们。换句话说，稳定的微型黑洞似乎并不构成任何威胁。
Clearly, the concern would be that these micro black holes would somehow be stable “accretors”—objects that could gather matter, pull it into themselves, and grow—and start gobbling up nearby matter and, eventually, the Earth. But if there were such things as stable micro black holes, they would already have been created by enormously energetic cosmic rays (which do exist) smacking into neutron stars and white dwarfs—where they would have taken up residence. And since white dwarfs and neutron stars appear stable on a time scale of hundreds of millions, if not billions of years, there don’t seem to be any tiny black holes eating them up from within. In other words, stable micro black holes appear to pose zero threat.
另一方面，如果没有额外维度理论，质量小于2 × 10⁻⁵克（称为普朗克质量）的黑洞根本无法被创造出来。也就是说，目前还没有任何物理学理论能够解释如此小质量的黑洞；我们需要量子引力理论，而这种理论并不存在。因此，对于质量为2 × 10⁻²⁰克的微型黑洞，史瓦西半径是多少这个问题也毫无意义。
On the other hand, without the theory of extra dimensions, black holes with a mass smaller than 2 × 10–5 grams (called the Planck mass) could not even be created. That is to say, there is no physics (yet) that can deal with black holes of such small mass; we would need a theory of quantum gravity, which doesn’t exist. Thus the question of what the Schwarzschild radius would be for a 2 × 10–20 gram micro black hole is also meaningless.
斯蒂芬·霍金已经证明黑洞可以蒸发。黑洞的质量越小，蒸发速度越快。一个质量为30个太阳质量的黑洞大约会在10⁷¹年内蒸发。一个质量为10亿个太阳质量的超大质量黑洞大约能存在10⁹³年！那么你可能会问，一个质量为2 × 10⁻²⁰克的微型黑洞需要多长时间才能蒸发呢？这是一个很好的问题，但没有人知道答案——霍金的理论不适用于质量小于普朗克质量的黑洞。不过，出于好奇，质量为2 × 10⁻⁵克的黑洞的寿命约为10⁻³⁹秒。所以看起来它们的蒸发速度比产生它们所需的时间还要快。换句话说，它们甚至无法被产生。
Stephen Hawking has shown that black holes can evaporate. The lower the mass of a black hole, the faster it will evaporate. A black hole of 30 solar masses would evaporate in about 1071 years. A supermassive black hole of 1 billion solar masses would last about 1093 years! So you may ask, how long would it take for a micro black hole of mass 2 × 10–20 grams to evaporate? It’s an excellent question, but no one knows the answer—Hawking’s theory does not work in the domain of black hole masses lower than the Planck mass. But, just for curiosity’s sake, the lifetime of a black hole of 2 × 10–5 grams is about 10–39 seconds. So it seems that they evaporate faster than the time it takes to produce them. In other words, they cannot even be produced.
显然没有必要担心可能存在的 2 × 10 –20克 LHC 微型黑洞。
It clearly seems unnecessary to worry about possible 2 × 10–20 gram LHC micro black holes.
我知道这并没有阻止人们提起诉讼，试图阻止大型强子对撞机（LHC）的运行。然而，这让我担忧科学家与普通民众之间的距离，以及我们科学家在解释自身研究成果方面做得多么糟糕。即便世界上一些最优秀的物理学家研究过这个问题，并解释了它为何不会造成任何问题，记者和政客们仍然凭空捏造各种场景，煽动公众恐慌。在某种程度上，科幻小说似乎比科学更有影响力。
I realize that this didn’t stop people from suing to prevent the LHC from starting operations. It makes me worry, however, about the distance between scientists and the rest of humanity and what a lousy job we scientists have done of explaining what we do. Even when some of the best physicists in the world studied the issue and explained why it wouldn’t pose any problems, journalists and politicians invented scenarios and fanned public fears on the basis of almost nothing. Science fiction at some level appears more powerful than science.
我认为，没有什么比黑洞更奇特的了。至少中子星还能通过其表面展现自身。中子星仿佛在说：“我在这里，我可以向你们展示我有一个表面。”而黑洞没有表面，也不发射任何物质（除了霍金辐射，但这种辐射从未被观测到）。
There’s nothing more bizarre than a black hole, I think. At least a neutron star makes itself known by its surface. A neutron star says, in a way, “Here I am, and I can show you that I have a surface.” A black hole has no surface and emits nothing at all (apart from Hawking radiation, which has never been observed).
一些黑洞被一个被称为吸积盘的扁平物质环（见下一章）包围，它们为何会喷射出能量极高的粒子流，且喷射方向垂直于吸积盘平面，但并非来自事件视界内部，这仍然是一个未解之谜。请看这张图片：www.wired.com/wiredscience/2009/01/spectacular-new/。
Why some black holes, surrounded by a flattish ring of matter known as an accretion disk (see the next chapter), shoot out extremely high energy jets of particles perpendicular to the plane of the accretion disk, though not from inside the event horizon, is one of the great unsolved mysteries. Take a look at this image: www.wired.com/wiredscience/2009/01/spectacular-new/.
关于黑洞内部，也就是事件视界之内的一切，我们都必须通过数学推导来理解。毕竟，没有任何东西能够逃逸出来，所以我们无法从黑洞内部获取任何信息——一些幽默的物理学家称之为“宇宙审查”。黑洞隐藏在它自己的洞穴之中。一旦你穿过事件视界，就永远无法逃脱——你甚至无法向外发送任何信号。如果你穿过了超大质量黑洞的事件视界，你甚至不会意识到自己已经越过了它。它没有沟渠，没有墙壁，也没有需要你走过的平台。当你越过视界时，你所处的环境不会发生任何突变。尽管如此，因为涉及到相对论物理学，如果你看你的手表，你不会看到它停止，也不会看到它走得更快或更慢。
Everything about the interior of a black hole, inside the event horizon, we have to derive mathematically. After all, nothing can come out, so we receive no information from inside the black hole—what some physicists with a sense of humor call “cosmic censorship.” The black hole is hidden inside its own cave. Once you fall through the event horizon, you can never get out—you can’t even send a signal out. If you’ve fallen through the event horizon of a supermassive black hole, you wouldn’t even know that you’ve passed the event horizon. It doesn’t have a ditch, or a wall, or a ledge you need to walk over. Nothing in your local environment changes abruptly when you cross the horizon. Despite all the relativistic physics involved, if you are looking at your wristwatch you wouldn’t see it stop, or appear to go faster or slower.
对于远处观察你的人来说，情况截然不同。他们看到的并非你本人；他们的眼睛接收到的是你身体发出的光所携带的影像，这些光从黑洞的引力井中爬升而出。随着你越来越接近事件视界，引力井也越来越深。光必须消耗更多的能量才能爬出引力井，并经历越来越大的引力红移。所有发射的电磁辐射都会向越来越长的波长（更低的频率）移动。你会看起来越来越红，然后随着你的辐射向越来越长的波长移动，例如红外线，再到越来越长的无线电波，最终当你越过事件视界时，所有波长都将趋于无穷大，你也就消失了。因此，甚至在你越过事件视界之前，对于远处的观察者来说，你实际上就已经消失了。
For someone watching you from a distance, the situation is very different. What they see is not you; their eyes are receiving the images of you carried by light that leaves your body and climbs its way out of the black hole’s gravity well. As you get closer and closer to the horizon, the well gets deeper and deeper. Light has to expend more of its energy climbing out of the well, and experiences more and more gravitational redshift. All emitted electromagnetic radiation shifts to longer and longer wavelengths (lower frequencies). You would look redder and redder, and then you would disappear as your emissions would move into longer and longer wavelengths, such as infrared light and then longer and longer radio waves and all wavelengths would become infinity as you cross the event horizon. So even before you crossed the threshold, to the distant observer you would have effectively disappeared.
远处的观测者还测量到了一个完全出乎意料的现象：来自黑洞附近区域的光速会变慢！这并不违反相对论的任何基本假设：黑洞附近的观测者始终测量到光速为c（约 186,000 英里/秒）。但远处的观测者测量到的光速小于c。你发出的光携带的你的影像到达远处观测者所需的时间，比你不在黑洞附近时要长。这带来了一个非常有趣的后果：观测者看到你随着接近事件视界而减速！事实上，你的影像到达她所需的时间越来越长，因此你的一切看起来都像是慢动作。对于地球上的观测者来说，你的速度、你的动作、你的手表，甚至你的心跳都会随着你接近事件视界而减慢，并在你到达事件视界时完全停止。如果不是因为引力红移导致你在地平线附近发出的光变得不可见，观察者就会看到你永远“冻结”在地平线表面。
The distant observer also measures a really unanticipated thing: light travels slower when it comes from a region close to the black hole! Now, this does not violate any postulates of relativity: local observers near the black hole always measure light traveling at the same speed c (about 186,000 miles per second). But distant observers measure the speed of light to be less than c. The images of you carried by the light you emitted toward your distant observer take longer to get to her than they would if you were not near a black hole. This has a very interesting consequence: the observer sees you slow down as you approach the horizon! In fact, the images of you are taking longer and longer to get to her, so everything about you seems in slow motion. To an observer on Earth, your speed, your movements, your watch, even your heartbeat slows down as you approach the event horizon, and will stop completely by the time you reach it. If it weren’t for the fact that the light you emit near the horizon becomes invisible due to the gravitational redshift, an observer would see you “frozen” on the horizon’s surface for all eternity.
为了简化计算，我忽略了多普勒频移，但随着你接近目标时速度不断增加，多普勒频移将会非常巨大。事件视界。事实上，当你越过事件视界时，你的运动速度将达到光速。（对于地球上的观察者来说，这种多普勒频移的影响类似于引力红移的影响。）
For simplicity I have been ignoring the Doppler shift, which will be enormous because of your ever-increasing speed as you approach the event horizon. In fact, as you cross the event horizon, you will be moving with the speed of light. (For an observer on Earth, the effects of this Doppler shift will be similar to the effects of the gravitational redshift.)
当你越过事件视界，与外界失去联系之后，你仍然可以看到外面的世界。来自事件视界之外的光线会因引力作用而发生频率升高、波长缩短的偏移，因此你会看到一个蓝移的宇宙。（如果你站在中子星表面，也会看到同样的现象。）然而，由于你正以极高的速度坠入其中，外部世界会远离你，因此外部世界也会发生红移（这是多普勒效应的结果）。那么最终结果会如何呢？是蓝移占上风，还是红移占上风？或者两者都不占上风？
After you have crossed the event horizon, when you can no longer communicate with the outside world, you will still be able to see out. Light coming from outside the event horizon would be gravitationally shifted to higher frequency and shorter wavelength, so you would see a blueshifted universe. (That would also be the case if you could stand on the surface of a neutron star as well, for the same reason.) However, since you are falling in at great speed, the outside world will be moving away from you, and thus the outside world will become redshifted as well (as a result of the Doppler effect). So what will be the result? Will the blueshift win or will the redshift win? Or will neither win?
我咨询了科罗拉多大学JILA的安德鲁·汉密尔顿，他是黑洞研究领域的权威专家。不出所料，答案并不简单。对于自由落体来说，蓝移和红移基本相互抵消，但外部世界看起来上方有红移，下方有红移，水平方向则有蓝移。（您或许会喜欢观看他制作的“进入史瓦西黑洞之旅”系列视频，了解物体落入黑洞的感受： http: //jila.colorado.edu/~ajsh/insidebh/schw.html。）
I asked Andrew Hamilton at the University of Colorado, JILA, who is a world authority on black holes and, as I expected, the answer is not so simple. The blueshift and redshift more or less cancel for a free faller, but the outside world looks redshifted above, redshifted below, and blue-shifted in horizontal directions. (You may enjoy looking at his “Journey into a Schwarzschild black hole” movies to see what it’s like to be an object falling into a black hole: http://jila.colorado.edu/~ajsh/insidebh/schw.html.)
然而，由于没有表面，所以根本无处可站。构成黑洞的所有物质都坍缩成一个点，一个奇点。那么潮汐力呢？你难道不会因为头部和脚趾受到的引力不同而感到痛苦不堪吗？（这和地球面向月球的一侧比远离月球的一侧受到更大的引力效应相同；这导致了地球上的潮汐。）
There wouldn’t be anyplace to stand, however, since there’s no surface. All the matter that created the black hole has collapsed into a point, a singularity. What about the tidal forces—wouldn’t you be torn to bits by the fact that there will be a difference between the gravitational force on your head and your toes? (It’s the same effect as the side of the Earth facing the Moon experiencing a larger attractive force than the side of the Earth that is farther away from the Moon; this causes tides on Earth.)
的确，你会被撕成碎片；一个质量为3个太阳质量的史瓦西黑洞会在你越过事件视界前0.15秒将你撕成碎片。这种现象被形象地称为“意大利面化”，指的是你的身体被拉伸到难以想象的程度。一旦你越过事件视界，你身体的各个部分将会……大约0.00001秒后，你将到达奇点，届时你会被压缩成一个密度无限大的点。对于一个质量为400万个太阳质量的黑洞，比如我们银河系中心的那个，你会安全地穿过事件视界，至少一开始不会有任何问题，但迟早你会像意大利面条一样被撕碎！（相信我，这“迟早”发生，因为在那之前你只剩下大约13秒的时间，然后，再过0.15秒，你就会到达奇点。）
Indeed, you would be torn to bits; a Schwarzschild black hole of 3 solar masses would rip you apart 0.15 seconds before you crossed the event horizon. This phenomenon is very graphically called spaghettification and involves your body being stretched beyond imagining. Once you have crossed the event horizon, the various pieces of your body will reach the singularity in about 0.00001 seconds, at which time you will be crushed into a point of infinite density. For a 4-million-solar-mass black hole, like the one at the center of our galaxy, you would safely cross the event horizon without having any problems at all, at least at first, but sooner or later you will be shredded spaghetti style! (Believe me, it will be “sooner,” because you have only about 13 seconds left before that happens and then, 0.15 seconds later, you will reach the singularity.)
黑洞的概念对所有人来说都非常奇特，尤其是对许多观测黑洞的天体物理学家而言（例如我的两位前研究生杰弗里·麦克林托克和乔恩·米勒）。我们知道恒星级黑洞的存在。它们于1971年被发现，当时光学天文学家证实天鹅座X-1是一个双星系统，其中一颗恒星就是黑洞！我将在下一章详细讲解。准备好了吗？
The whole idea of black holes is truly bizarre for everyone, but especially for the many astrophysicists who observe them (such as my former graduate students Jeffrey McClintock and Jon Miller). We know that stellar-mass black holes exist. They were discovered in 1971 when optical astronomers demonstrated that Cyg X-1 is a binary star system and that one of the two stars is a black hole! I will tell you all about this in the next chapter. Ready?
第十三章
CHAPTER 13
天体芭蕾
Celestial Ballet
现在你大概已经知道，无论用望远镜还是其他任何方式观测，你在天空中看到的许多星星都比我们熟悉的太阳要复杂得多。你可能不知道，你所看到的星星中大约有三分之一根本不是单颗恒星，而是我们所说的双星系统：两颗恒星因引力束缚在一起，彼此绕转。换句话说，当你仰望夜空时，你看到的星星中大约有三分之一是双星系统——尽管它们看起来像一颗恒星。宇宙中甚至还有三星系统——三颗恒星彼此绕转——尽管它们远不如双星系统常见。由于我们银河系中许多明亮的X射线源最终都被证实是双星系统，所以我对它们进行了很多研究。它们非常迷人。
It will come as no surprise to you by now that many of the stars you see in the heavens, with or without a telescope of any kind, are a lot more complicated than distant versions of our own familiar Sun. You may not know that about a third of what you see aren’t even single stars at all, but rather what we call binaries: pairs of stars that are gravitationally bound together, orbiting each other. In other words, when you look up at the night sky about a third of the stars you see are binary systems—even though they appear to you as a single star. There are even triple star systems—three stars orbiting one another—out there as well, though they are not nearly as common. Because many of the bright X-ray sources in our galaxy turned out to be binary systems, I had many dealings with them. They are fascinating.
双星系统中的每颗恒星都围绕着我们称之为双星质心的点运行，这个质心位于两颗恒星之间。如果两颗恒星的质量相等，那么质心到两颗恒星中心的距离也相等。如果质量不同，那么质心会更靠近质量较大的那颗恒星。由于两颗恒星都会绕着同一轨道运行，因此它们的轨道是相等的。在相同的时间内，质量较大的恒星的轨道速度必然低于质量较小的恒星。
Each star in a binary system travels around what we call the center of mass of the binary, a point located between the two stars. If the two stars have equal mass, then the center of mass is at equal distance from the center of both stars. If the masses are not the same, then the center of mass is closer to the more massive star. Since both complete an orbit in exactly the same amount of time, the more massive star must have a lower orbital speed than the less massive one.
为了形象地理解这个原理，想象一个哑铃，两端质量相等，中间用一根杆连接，围绕其中点旋转。现在想象一个新的哑铃，一端重2磅，另一端重10磅。这个哑铃的质心非常靠近较重的一端，所以当它旋转时，你会发现质量较大的一端轨道较小，而质量较小的一端在相同时间内需要运行更远的距离。如果把两端换成恒星，你会发现质量较小的恒星绕其轨道运行的速度是质量较大、笨重的伴星的五倍。
To visualize this principle, imagine a dumbbell with a bar connecting two ends of equal mass, rotating around its midpoint. Now imagine a new dumbbell, 2 pounds on one end, 10 pounds on the other. The center of mass of this dumbbell is quite close to the heavier end, so when it rotates you can see that the larger mass has a smaller orbit, and that the smaller mass has farther to go in the same time. If these are stars instead of weighted ends, you can see that the lower-mass star zooms around its orbit at five times the speed of its larger, clunkier companion.
如果其中一颗恒星的质量远大于其伴星，那么该系统的质心甚至可以位于质量较大的那颗恒星内部。以地球和月球（一个双星系统）为例，其质心位于地球表面以下约1700公里（略多于1000英里）处。（我在附录2中提到过这一点。）
If one of the stars is much more massive than its companion, the center of mass of the system can even lie within the more massive star. In the case of the Earth and Moon (which is a binary system), the center of mass is about 1,700 kilometers (a little more than a thousand miles) below the Earth’s surface. (I mention this in appendix 2.)
天狼星是天空中最亮的恒星（距离我们约 8.6 光年），它是一个双星系统，由两颗恒星组成，分别称为天狼星 A 和天狼星 B。它们围绕着共同的质心运行，大约每 50 年运行一次（我们称之为轨道周期）。
Sirius, the brightest star in the sky (at a distance from us of about 8.6 light-years), is a binary system made up of two stars known as Sirius A and Sirius B. They orbit their common center of mass about once every fifty years (we call this the orbital period).
我们如何判断观测到的是一个双星系统？肉眼无法分别看到双星系统中的两颗恒星。但根据双星系统的距离和我们所用望远镜的功率，有时我们可以通过观察两颗恒星的分离情况来确认这一点。
How can we tell that we’re looking at a binary system? We can’t see binaries separately with the naked eye. Depending on the distance of the system and the power of the telescopes we’re using, we can sometimes get visual confirmation by seeing the two stars as separate.
德国著名数学家和天文学家弗里德里希·威廉·贝塞尔预言，天空中最亮的恒星天狼星是一个双星系统，由一颗可见星和一颗不可见星组成。他的这一结论基于其精确的天文观测——他是1838年第一个进行视差观测的人（他险胜亨德森——参见第二章）。1844年，他给亚历山大·冯·洪堡写了一封著名的信：“我坚信天狼星是一个双星系统，由一颗可见星和一颗不可见星组成。没有理由认为亮度是宇宙天体的本质属性。无数恒星的可见性并不能反驳天狼星不可见性的观点。”还有无数其他人。” 这句话意味深长；我们看不见的东西，通常不会相信。贝塞尔开创了我们现在所说的“不可见天文学”。
The famous German mathematician and astronomer Friedrich Wilhelm Bessel predicted that the brightest star in the sky, Sirius, was a binary system, consisting of a visible and an invisible star. He had concluded this based on his precise astronomical observations—he was the first in 1838 to make parallax observations (he narrowly beat Henderson—see chapter 2). In 1844 he wrote a famous letter to Alexander von Humboldt: “I adhere to the conviction that the star Sirius is a binary system consisting of a visible and an invisible star. There is no reason to suppose that luminosity is an essential quality of cosmic bodies. Visibility of countless stars is no argument against the invisibility of countless others.” This is a statement of profound depth; what we can’t see, we usually don’t believe. Bessel started what we now call the astronomy of the invisible.
直到 1862 年，人们才真正看到了这颗“隐形”的伴星（被称为天狼星 B）。当时，阿尔文·克拉克在我的家乡马萨诸塞州剑桥市测试一台全新的 18.5 英寸望远镜（当时最大的望远镜，由他父亲的公司制造）。为了进行测试，他用望远镜对准了正在波士顿天际线上升的天狼星，结果发现了天狼星 B（它比天狼星 A 暗一万倍）。
No one actually saw the “invisible” companion (called Sirius B) until 1862, when Alvan Clark was testing a brand new 18.5-inch telescope (the largest one at the time, made by his father’s company) in my hometown, Cambridge, Massachusetts. He turned the telescope on Sirius as it was rising above the Boston skyline, for a test, and discovered Sirius B (it was ten thousand times fainter than Sirius A).
感谢恒星光谱学：蓝移和红移
Thank Goodness for Stellar Spectroscopy: Blueshifts and Redshifts
迄今为止，确定恒星是否为双星系统（尤其是在遥远的情况下）最常用的方法是利用光谱学测量多普勒频移。光谱学或许是天体物理学中最强大的工具，而多普勒频移也是过去几个世纪以来天文学领域最重要的发现之一。
By far the most common method of figuring out that stars are binaries, especially if they’re distant, is by using spectroscopy and measuring what’s known as the Doppler shift. There may be no more powerful astrophysical tool than spectroscopy, and no more important discovery in astronomy in the past several centuries than the Doppler shift.
你已经知道，物体温度足够高时会发出可见光（黑体辐射）。就像棱镜分解阳光一样，构成彩虹的雨滴（第五章）会呈现出从一端的红色到另一端的紫色的连续颜色，这被称为光谱。如果你分解恒星发出的光，也会看到光谱，但光谱中各种颜色的强度可能并不相同。例如，恒星温度越低，它的颜色（以及它的光谱）就越红。参宿四（位于猎户座）的温度只有2000开尔文，是天空中最红的恒星之一。而参宿五（同样位于猎户座）的温度则高达28000开尔文，是天空中最蓝、最亮的恒星之一，通常被称为“亚马逊星”。
You already know that when objects are hot enough they will emit visible light (blackbody radiation). By decomposing sunlight in the way a prism does, the raindrops that make up a rainbow (chapter 5) show you a continuum of colors from red at one end to violet at the other, called a spectrum. If you decompose the light from a star, you will also see a spectrum, but it may not have all the colors in equal strengths. The cooler the star, for example, the redder the star (and its spectrum) will be. The temperature of Betelgeuse (in the constellation Orion) is only 2,000 kelvin; it’s among the reddest stars in the sky. The temperature of Bellatrix, on the other hand, also in Orion, is 28,000 kelvin; it’s among the bluest and brightest stars in the sky and is often called the Amazon Star.
仔细观察恒星光谱，会发现一些狭窄的间隙，在这些间隙中颜色减弱甚至完全消失，我们称之为吸收线。太阳光谱中就包含了数千条这样的吸收线。这些现象是由恒星大气层中多种不同的元素造成的。如你所知，原子由原子核和电子组成。电子的能量并非任意的；它们具有离散的能级——它们的能量不可能介于这些不同的能级之间。换句话说，它们的能量是“量子化的”——正是这个术语催生了量子力学领域。
A close look at stellar spectra shows narrow gaps where colors are reduced or even completely absent, which we call absorption lines. The spectrum of the Sun shows thousands of such absorption lines. These are caused by the many different elements in the atmospheres of the stars. Atoms, as you know, are made of nuclei and electrons. The electrons cannot just have any energy; they have discrete energy levels—they cannot have energies in between these distinct levels. Their energies, in other words, are “quantized”—the term that gives rise to the field of quantum mechanics.
中性氢原子只有一个电子。如果用光照射它，这个电子可以通过吸收光子的能量从一个能级跃迁到更高的能级。但由于电子能级的量子化特性，并非任何能量的光子都能使电子跃迁。只有那些能量（即频率和波长）恰好合适的光子才能使电子发生量子跃迁。这个过程（称为共振吸收）会吸收这些光子，并在连续光谱中产生一个频率缺失，我们称之为吸收线。
Neutral hydrogen has one electron. If it is bombarded with light, this electron can jump from one energy level to a higher energy level by absorbing the energy of a light photon. But because of the quantization of the energy levels of the electron, this cannot happen with photons of just any energy. Only those photons that have just the right energy (thus exactly the right frequency and wavelength) for the electron to make the quantum jump from one level to another will do. This process (called resonance absorption) kills these photons and creates an absence at that frequency in the continuum spectrum, which we call an absorption line.
氢在恒星光谱的可见光部分可以产生四条吸收线（波长或颜色精确可知）。大多数元素由于电子数远多于氢，因此可以产生更多的吸收线。事实上，每种元素都有其独特的吸收线组合，这就像一种“指纹”。我们通过在实验室中研究和测量这些吸收线，可以非常准确地了解它们。因此，仔细研究恒星光谱中的吸收线可以告诉我们恒星大气层中存在哪些元素。
Hydrogen can produce four absorption lines (at precisely known wavelengths, or colors) in the visible part of a stellar spectrum. Most elements can produce many more lines, because they have lots more electrons than hydrogen. In fact, each element has its own unique combination of absorption lines, which amounts to a fingerprint. We know these very well from studying and measuring them in the laboratory. A careful study of the absorption lines in a stellar spectrum can therefore tell us which elements are present in the star’s atmosphere.
然而，当一颗恒星远离我们时，一种被称为多普勒效应的现象会导致恒星的整个光谱（包括吸收线）向光谱的红色区域移动（我们称之为红移）。相反，如果光谱发生蓝移，则表明恒星正在向我们靠近。通过精确测量恒星吸收线波长的偏移量，我们可以计算出恒星相对于我们的运动速度。
However, when a star moves away from us, the phenomenon known as the Doppler shift causes the star’s entire spectrum (including the absorption lines) to shift toward the red part of the spectrum (we call this redshift). If, by contrast, the spectrum is blueshifted, we know the star is moving toward us. By carefully measuring the amount of shift in the wavelength of a star’s absorption lines, we can calculate the speed with which the star is moving relative to us.
例如，如果我们观测一个双星系统，每颗恒星在其公转周期的一半时间内会朝向我们运动，另一半时间内则会远离我们运动。它的伴星则会做完全相反的事情。如果两颗恒星都很明亮，那么它们之间的运动轨迹就会有所不同。足够之后，我们就能在光谱中看到红移和蓝移的吸收线。这表明我们正在观测一个双星系统。但由于恒星的轨道运动，这些吸收线会在光谱上发生移动。例如，如果轨道周期为20年，那么每条吸收线将在20年内完成一次完整的偏移（10年的红移和10年的蓝移）。
If we observe a binary system, for example, each star will move toward us for half of its orbit and away from us during the other half. Its companion will be doing exactly the opposite. If both stars are bright enough, we will see redshifted and blueshifted absorption lines in the spectrum. That would tell us that we are looking at a binary system. But the absorption lines will be moving along the spectrum due to the orbital motion of the stars. As an example, if the orbital period is twenty years, each absorption line will make a complete excursion in twenty years (ten years of redshift and ten years of blueshift).
即使我们只能观测到红移（或蓝移）吸收线，只要吸收线在光谱中来回移动，我们仍然可以确定这是一个双星系统；测量吸收线完成一个完整周期所需的时间，就能得出恒星的轨道周期。这种情况何时会发生呢？当其中一颗恒星亮度太低，无法从地球上的可见光观测到时。
If we can see only redshifted (or only blueshifted) absorption lines, we still know it is a binary system if we see the absorption lines move back and forth in the spectrum; a measurement of the time it takes for a full cycle of the lines will tell us the orbital period of the star. When would this happen? In the event that one star is too faint to be seen from Earth in optical light.
现在让我们回到X射线源。
Let’s now return to our X-ray sources.
什克洛夫斯基及其后
Shklovsky and Beyond
早在 1967 年，俄罗斯物理学家约瑟夫·什克洛夫斯基就提出了天蝎座 X-1 的模型。“从所有特征来看，该模型对应于一颗处于吸积状态的中子星……这种吸积的天然且非常有效的气体供应来源，是从密近双星系统中的次级星流向作为中子星的主星的气体流。”
Way back in 1967, the Russian physicist Joseph Shklovsky had proposed a model for Sco X-1. “By all its characteristics, this model corresponds to a neutron star in a state of accretion… the natural and very efficient supply of gas for such an accretion is a stream of gas which flows from a secondary component of a close binary system toward the primary component which is a neutron star.”
我知道这些话可能不会让你觉得惊天动地。它们是用略显枯燥的天体物理学专业术语写成的，这无疑也加剧了这种感觉。但几乎所有领域的专业人士都是这样交流的。我在课堂上的目的，以及我写这本书的主要原因，就是要把我的物理学同行们那些真正令人惊叹、具有开创性，有时甚至是革命性的发现，转化为聪明好奇的普通人能够真正理解的概念和语言——在专业科学家的世界和你们的世界之间架起一座桥梁。我们当中太多人似乎更喜欢只和同行交流，这使得大多数人——即使是那些真正想了解科学的人——很难进入我们的世界。
I realize these lines may not strike you as earthshaking. It doesn’t help that they are written in the rather dry technical language of astrophysics. But that’s the way professionals in just about any field talk to one another. My purpose in the classroom, and the main reason I’ve written this book, is to translate the truly astounding, groundbreaking, sometimes even revolutionary discoveries of my fellow physicists into concepts and language intelligent, curious laypeople can really get hold of—to make a bridge between the world of professional scientists and your world. Too many of us seem to prefer talking only to our peers and make it awfully difficult for most people—even those who really want to understand science—to enter our world.
那么，让我们来看看什克洛夫斯基的设想：一个由一颗中子星和一颗伴星组成的双星系统，物质正从伴星流向中子星。这样一来，中子星就处于“吸积状态”——换句话说，它会从伴星（即供体星）吸积物质。多么奇特的想法，对吧？
So let’s take Shklovsky’s idea and see what he was proposing: a binary star system composed of a neutron star and a companion from which matter was flowing to the neutron star. The neutron star would then be “in a state of accretion”—in other words, it would be accreting matter from its companion, the donor star. What a bizarre idea, right?
事实证明，什克洛夫斯基是对的。但有趣的是，他当时只是在讨论天蝎座X-1，我们大多数人并没有太认真对待他的观点。但理论往往如此。我想，如果我说天体物理学中绝大多数理论最终都被证明是错误的，应该不会冒犯到我的理论物理学家同行。所以，我们这些从事观测天体物理学的人当然不会太在意这些理论。
Shklovsky turned out to be right. But here’s the funny thing. He was only talking about Sco X-1 at the time, and most of us didn’t take his idea too seriously. But that’s often the case with theory. I don’t think I would be offending any of my theoretician colleagues by saying that the great majority of theory in astrophysics turns out to be wrong. So of course many of us in observational astrophysics don’t pay much attention to most of it.
事实证明，吸积中子星实际上是产生X射线的理想环境。我们是如何发现什克洛夫斯基的理论是正确的呢？
It turns out that accreting neutron stars are in fact the perfect environments to produce X-rays. How did we find out that Shklovsky was right?
直到上世纪七十年代初，天文学家才最终确定一些X射线源的双星性质——但这并不一定意味着它们就是吸积中子星。第一个揭示其奥秘的X射线源是天鹅座X-1，它后来被证明是X射线天文学中最重要的天体之一。天鹅座X-1于1964年的一次火箭飞行中被发现，它是一个非常明亮且强大的X射线源，因此自那时起就一直吸引着X射线天文学家的关注。
It took until the early seventies for astronomers to nail down the binary nature of some X-ray sources—but that didn’t necessarily mean that they were accreting neutron stars. The very first source to reveal its secrets was Cyg X-1, and it turned out to be one of the most important in all of X-ray astronomy. Discovered during a rocket flight in 1964, it is a very bright and powerful source of X-rays, so it has attracted the attention of X-ray astronomers ever since.
1971年，射电天文学家发现了天鹅座X-1的射电波。他们的射电望远镜将天鹅座X-1的位置精确定位在天空中一个约350平方角秒的区域（误差框）内，比通过追踪其X射线所能达到的范围小了大约20倍。他们开始寻找它的光学对应体。换句话说，他们想在可见光波段观测到这颗产生神秘X射线的恒星。
Radio astronomers then discovered radio waves from Cyg X-1 in 1971. Their radio telescopes pinpointed Cyg X-1’s position to a region (an error box) in the sky of about 350 square arc seconds, about twenty times smaller than had been possible by tracking its X-rays. They went looking for its optical counterpart. In other words, they wanted to see, in visible light, the star that was generating the mysterious X-rays.
在射电误差范围内，有一颗非常明亮的蓝色超巨星，名为HDE 226868。根据这颗恒星的类型，天文学家可以将其与其他非常相似的恒星进行比较，从而对其质量做出相当准确的估算。包括世界著名天文学家艾伦·桑德奇在内的五位天文学家得出结论，HDE 226868只是一颗“普通的B0型超巨星”。他们说这颗星没有任何特殊之处”，并忽略了它是天鹅座 X-1 的光学对应体这一事实。其他（当时不太出名的）光学天文学家更仔细地研究了这颗恒星，并取得了一些惊人的发现。
There was a very bright blue supergiant known as HDE 226868 in the radio error box. Given the kind of star it was, astronomers could make comparisons with other very similar stars to make a pretty good estimate of its mass. Five astronomers, including the world-famous Allan Sandage, concluded that HDE 226868 was just a “normal B0 supergiant, with no peculiarities,” and they dismissed the fact that it was the optical counterpart of Cyg X-1. Other (at the time less famous) optical astronomers examined the star more closely and made some earthshaking discoveries.
他们发现这颗恒星是双星系统中的一员，轨道周期为5.6天。他们的论证是正确的：该双星系统发出的强X射线辐射是由于光学恒星（供体星）向一个非常小的致密天体吸积气体所致。只有气体流向一个质量巨大但体积很小的天体才能解释如此丰富的X射线辐射。
They discovered that the star was a member of a binary system with an orbital period of 5.6 days. They argued correctly that the strong X-ray flux from this binary system was due to the accretion of gas from the optical star (the donor) to a very small—compact—object. Only a gas flow onto a massive but very small object could explain the copious X-ray flux.
他们测量了伴星光谱中吸收线的多普勒频移，并分析了它绕地球轨道运动时的变化（记住，当它向地球靠近时，光谱会向蓝端移动；当它远离地球时，光谱会向红端移动）。他们得出结论：产生X射线的伴星质量太大，不可能是中子星或白矮星（另一种致密、密度极高的恒星，例如天狼星B）。那么，如果它既不是中子星也不是白矮星，而且质量甚至比中子星还要大，那它还能是什么呢？当然——黑洞！这就是他们提出的解释。
They made Doppler-shift measurements of absorption lines in the spectrum of the donor star as it moved around in its orbit (remember, as it moved toward Earth, the spectra would shift toward the blue end, and as it moved away, it would shift toward the red) and concluded that the X-ray-generating companion star was too massive to be either a neutron star or a white dwarf (another compact, very dense star, like Sirius B). Well, if it couldn’t be either of those, and it was even more massive than a neutron star, what else could it be? Of course—a black hole! And that’s what they proposed.
然而，作为观测科学家，他们在陈述结论时更为谨慎。路易丝·韦伯斯特和保罗·默丁的发现于1972年1月7日发表在《自然》杂志上，他们是这样描述的：“伴星的质量可能大于两个太阳质量，因此我们必然会推测它也可能是一个黑洞。”一个月后，汤姆·博尔顿在《自然》杂志上写道：“这极有可能表明，伴星（吸积体）是一个黑洞。”插图中可以看到天鹅座X-1的艺术想象图。
As observational scientists, however, they stated their conclusions more circumspectly. Louise Webster and Paul Murdin, whose discovery ran in Nature on January 7, 1972, put it this way: “The mass of the companion being probably larger than 2 solar masses, it is inevitable that we should also speculate that it might be a black hole.” Here’s what Tom Bolton wrote a month later in Nature: “This raises the distinct possibility that the secondary [the accretor] is a black hole.” A picture of an artistic impression of Cyg X-1 can be seen in the insert.
因此，这几位杰出的天文学家——英国的韦伯斯特和默丁，以及多伦多的博尔顿——共同发现了X射线双星系统，并找到了我们银河系中的第一个黑洞。（博尔顿为此感到非常自豪，他的车牌号“天鹅座X-1”用了好几年。）
So these wonderful astronomers, Webster and Murdin in England and Bolton in Toronto, shared the discovery of X-ray binaries and finding the first black hole in our galaxy. (Bolton was so proud, he had the license plate Cyg X-1 for a number of years.)
我一直觉得很奇怪，他们那项惊人的发现竟然从未获得过任何重大奖项。毕竟，他们进入这个领域时……他们找到了它的核心，而且他们是第一个！他们成功探测到了第一个X射线双星系统。他们还说吸积体很可能是一个黑洞。真是了不起的成就！
I’ve always thought it was odd that they never received a major prize for their absolutely phenomenal discovery. After all, they hit the field at its heart, and they were first! They nailed the first X-ray binary system. And they said that the accretor was probably a black hole. What a piece of work!
1975年，史蒂芬·霍金与他的朋友、理论物理学家基普·索恩打赌，天鹅座X-1根本不是黑洞——尽管当时大多数天文学家都认为它是。十五年后，他最终承认了赌约，我想他应该很高兴，因为他的大部分研究都围绕着黑洞展开。天鹅座X-1中黑洞质量的最新（即将发表）也是最精确的测量结果约为15个太阳质量（杰里·奥罗斯和我以前的学生杰夫·麦克林托克的私人交流）。
In 1975 none other than Stephen Hawking bet his friend, fellow theoretical physicist Kip Thorne, that Cyg X-1 wasn’t a black hole at all—even though most astronomers thought it was by then. He eventually conceded the bet, fifteen years later, I think to his own delight, since so much of his work has revolved around black holes. The most recent (soon to be published) and most accurate measurement of the mass of the black hole in Cyg X-1 is about 15 solar masses (private communication from Jerry Orosz and my former student Jeff McClintock).
如果你足够机敏，我知道你肯定已经在想：“等等！你刚才说黑洞不会发射任何东西，没有任何东西能逃脱它们的引力场——它们怎么会发射X射线呢？” 这是一个很好的问题，我保证最终会解答，但这里先给你一个预告：黑洞发射的X射线并非来自事件视界内部——它们是由进入黑洞的物质在运动过程中发射的。虽然黑洞可以解释我们对天鹅座X-1的观测结果，但它无法解释其他双星系统发射的X射线。要解释这些现象，我们需要中子星双星系统，而中子星双星系统正是通过神奇的卫星“乌呼鲁”发现的。
If you’re sharp, I know you’re already thinking, “Hold it! You just said black holes don’t emit anything, that nothing can escape their gravitational field—how can they emit X-rays?” Terrific question, which I promise to answer eventually, but here’s a preview: the X-rays emitted by a black hole do not come from inside the event horizon—they’re emitted by matter on the way into the black hole. While a black hole explained our observations of Cyg X-1, it could not explain what was seen in terms of X-ray emission from other binary stars. For that we needed neutron star binaries, which were discovered with the wonderful satellite Uhuru.
1970年12月，第一颗完全用于X射线天文学的卫星进入轨道，X射线天文学领域由此发生了翻天覆地的变化。这颗卫星于肯尼亚独立七周年之际从肯尼亚发射升空，被命名为“乌胡鲁”（Uhuru），在斯瓦希里语中意为“自由”。
The field of X-ray astronomy dramatically changed in December 1970, when the first satellite totally dedicated to X-ray astronomy went into orbit. Launched from Kenya on the seventh anniversary of Kenyan independence, the satellite was named Uhuru, Swahili for “freedom.”
乌胡鲁开启了一场至今仍在持续的革命。想想一颗卫星能做到什么：一年365天，一天24小时不间断观测，而且完全不受大气层的影响！乌胡鲁的观测方式，在六年前我们只能梦想。短短两年多时间，乌胡鲁就绘制出了X射线天空图，其探测器能够探测到比蟹状星云暗500倍、比天蝎座X-1暗1万倍的X射线源。它发现了339个这样的X射线源（在此之前，我们只发现了几十个），并提供了第一张完整的X射线天空图。
Uhuru began a revolution that hasn’t stopped to this day. Think about what a satellite could do. Observations 365 days a year, twenty-four hours a day, with no atmosphere at all! Uhuru was able to observe in ways we could only have dreamed about a half dozen years earlier. In just a little over two years, Uhuru mapped the X-ray sky with counters that could pick up sources five hundred times fainter than the Crab Nebula, ten thousand times fainter than Sco X-1. It found 339 of them (we’d only found several dozen before that) and provided the first X-ray map of the entire sky.
卫星天文台终于将我们从大气层的束缚中解放出来，重塑了我们对宇宙的认知。我们得以透过电磁波谱的各个波段观测深空及其中令人惊叹的天体。哈勃太空望远镜拓展了我们对可见光宇宙的认知，而一系列X射线天文台则拓展了我们对X射线宇宙的认知。如今，伽马射线天文台正在以更高的能量观测宇宙。
Freeing us at last from atmospheric shackles, satellite observatories have reshaped our view of the universe, as we learned to see deep space—and the astonishing objects it contains—through every area of the electromagnetic spectrum. The Hubble Space Telescope expanded our view of the optical universe, while a series of X-ray observatories did the same for the X-ray universe. Gamma-ray observatories are now observing the universe at even higher energies.
1971年，Uhuru卫星发现了来自半人马座Cen X-3的4.84秒脉动。在一天的时间里，Uhuru观测到X射线流量在大约一小时内变化了十倍。脉动周期先减小后增大，分别约为0.02%和0.04%，每次周期变化都发生在大约一小时内。这一切令人兴奋，但也令人费解。这些脉动不可能是旋转中子星造成的；已知中子星的自转周期非常稳定。已知的脉冲星中，没有任何一颗脉冲星的周期能在一小时内变化0.04%。
In 1971 Uhuru discovered 4.84-second pulsations from Cen X-3 (in the constellation Centaurus). During a one-day interval Uhuru observed a change in the X-ray flux by a factor of ten in about one hour. The period of the pulsations first decreased and then increased by about 0.02 and 0.04 percent, each change of period occurring in about an hour. All this was very exciting but also very puzzling. The pulsations couldn’t be the result of a spinning neutron star; their rotation periods were known to be steady like a rock. None of the known pulsars could possibly change their period by 0.04 percent in an hour.
当乌呼鲁研究小组后来发现半人马座X-3是一个轨道周期为2.09天的双星系统时，整个图景才得以完美呈现。4.84秒的脉动是由吸积中子星的自转引起的。证据确凿无疑。首先，他们清晰地观测到周期性出现的食（每2.09天一次），即中子星遮挡住供星，阻挡X射线辐射。其次，他们能够测量脉动周期的多普勒频移。当中子星朝向我们运动时，脉动周期略短；当它远离我们运动时，脉动周期略长。这些震撼人心的研究成果于1972年3月发表。所有这些都自然而然地解释了1971年论文中那些令人费解的现象。正如什克洛夫斯基对天蝎座X-1的预测：一个由供星和吸积中子星组成的双星系统。
The entire picture came together beautifully when the Uhuru group later discovered that Cen X-3 was a binary system with an orbital period of 2.09 days. The 4.84-second pulsations were due to the rotation of the accreting neutron star. The evidence was overwhelming. First, they clearly saw repetitive eclipses (every 2.09 days) when the neutron star hides behind the donor star, blocking the X-rays emissions. And second, they were able to measure the Doppler shift in the periods of the pulsations. When the neutron star is moving toward us, the pulsation period is a little shorter, a little longer when moving away. These earthshaking results were published in March 1972. All this naturally explained the phenomena that seemed so puzzling in the 1971 paper. It was just as Shklovsky had predicted for Sco X-1: a binary system with a donor star and an accreting neutron star.
同年晚些时候，贾科尼的研究小组又发现了一个新的辐射源——赫拉克勒斯X-1（或者我们更喜欢称之为赫尔X-1），它具有脉动和食现象。又一个中子星X射线双星系统！
Later that very same year, Giacconi’s group found yet another source, Hercules X-1 (or Her X-1, as we like to say), with pulsations and eclipses. Another neutron star X-ray binary!
这些发现绝对令人震惊，彻底改变了X射线技术。天文学领域，未来几十年内仍将占据主导地位。X射线双星非常罕见；我们银河系中，或许只有一亿分之一的双星系统是X射线双星。即便如此，我们现在知道银河系中存在数百个X射线双星系统。在大多数情况下，致密天体（吸积体）是白矮星或中子星，但至少有二十几个已知的系统中，吸积体是黑洞。
These were absolutely stunning discoveries that transformed X-ray astronomy, dominating the field for decades to come. X-ray binaries are very rare; perhaps only one in a hundred million binary stars in our galaxy is an X-ray binary. Even so, we now know that there are several hundred X-ray binaries in our galaxy. In most cases the compact object, the accretor, is a white dwarf or a neutron star, but there are at least two dozen known systems in which the accretor is a black hole.
还记得我们团队在1970年（乌呼鲁号发射之前）发现的2.3分钟周期吗？当时我们完全不明白这些周期性变化意味着什么。现在我们知道，GX 1+4是一个X射线双星系统，其轨道周期约为304天，而吸积中子星的自转周期约为2.3分钟。
Remember the 2.3-minute periodicity that my group discovered in 1970 (before the launch of Uhuru)? At the time we had no clue what these periodic changes meant. Well, we now know that GX 1+4 is an X-ray binary system with an orbital period of about 304 days, and the accreting neutron star spins around in about 2.3 minutes.
X射线双星：它们的工作原理
X-ray Binaries: How They Work
当一颗中子星与大小合适、距离合适的伴星相遇时，便能迸发出令人惊叹的宇宙奇观。在浩瀚的宇宙深处，即使是艾萨克·牛顿也无法想象的恒星，竟能翩翩起舞，演绎出美妙的景象，而这一切，都完全遵循着任何理科本科生都能理解的经典力学定律。
When a neutron star pairs up with the right-size donor star at the right distance, it can create some amazing fireworks. There, in the reaches of space, stars Isaac Newton could never even have imagined perform a beautiful dance, all the while utterly bound by the laws of classical mechanics any undergraduate science major can grasp.
为了更好地理解这一点，让我们从身边的例子开始。地球和月球是一个双星系统。如果你画一条连接地球中心和月球中心的直线，这条线上会有一个点，在这个点上，地球对月球的引力与对地球的引力大小相等、方向相反。如果你在这个点上，你受到的合力为零。如果你在这个点的一侧，你会落向地球；如果你在另一侧，你会落向月球。这个点有一个名字，我们称之为内拉格朗日点。当然，它离月球非常近，因为月球的质量大约只有地球的八十倍。
To understand this better, let’s start close to home. The Earth and the Moon are a binary system. If you draw a line from the center of the Earth to the center of the Moon, there is a point on that line where the gravitational force toward the Moon is equal but opposite to the gravitational force toward Earth. If you were there, the net force on you would be zero. If you were on one side of that point you would fall to Earth; if you were on the other side you would fall toward the Moon. That point has a name; we call it the inner Lagrangian point. Of course, it lies very close to the moon, because the Moon’s mass is about eighty times smaller than that of the Earth.
现在我们回到由吸积中子星和一颗体积大得多的供体星组成的X射线双星系统。如果这两颗恒星彼此非常接近，内拉格朗日点可能位于供体星表面以下。在这种情况下，供体星的部分物质将经历指向中子星的引力大于指向供体恒星中心的引力。因此，物质——高温氢气——将从供体恒星流向中子星。
Let’s now return to X-ray binaries consisting of an accreting neutron star and a much larger donor star. If the two stars are very close to each other, the inner Lagrangian point can lie below the surface of the donor star. If that is the case, some of the matter of the donor star will experience a gravitational force toward the neutron star that is larger than the gravitational force toward the center of the donor star. Consequently matter—hot hydrogen gas—will flow from the donor star to the neutron star.
由于这些恒星围绕它们的共同质心运行，物质无法直接落向中子星。在到达中子星表面之前，物质会进入围绕中子星的轨道，形成一个旋转的热气体盘，我们称之为吸积盘。吸积盘内环上的部分气体最终会落到中子星表面。
Since the stars are orbiting their common center of mass, the matter cannot fall directly toward the neutron star. Before it reaches the surface, the matter falls into an orbit around the neutron star, creating a spinning disk of hot gas that we call an accretion disk. Some of the gas on the inner ring of the disk ultimately finds its way down to the surface of the neutron star.
现在，一个有趣的物理原理涉及到了，你可能在其他领域已经有所了解。由于气体温度极高，它会发生电离，由带正电的质子和带负电的电子组成。但由于中子星拥有非常强的磁场，这些带电粒子被迫沿着磁力线运动，因此大部分等离子体最终会聚集在中子星的磁极，就像地球上的北极光一样。中子星的磁极（物质撞击中子星的地方）会变成温度高达数百万开尔文的热点，并辐射出X射线。由于磁极通常与自转轴的极点不重合（参见第12章），因此只有当热点正对着我们时，地球上才能接收到高强度的X射线辐射。由于中子星会自转，所以它看起来会脉动。
Now an interesting piece of physics gets involved that you are already familiar with in another context. Since the gas is very hot, it is ionized, consisting of positively charged protons and negatively charged electrons. But since the neutron stars have very strong magnetic fields, these charged particles are forced to follow the star’s magnetic field lines, so most of this plasma ends up at the magnetic poles of the neutron star, like the aurora borealis on Earth. The neutron star’s magnetic poles (where matter crashes onto the neutron star) become hot spots with temperatures of millions of degrees kelvin, emitting X-rays. And as magnetic poles generally do not coincide with the poles of the axis of rotation (see chapter 12), we on Earth will only receive a high X-ray flux when a hot spot is facing us. Since the neutron star rotates, it appears to pulsate.
每个X射线双星系统都有一个围绕吸积体运行的吸积盘，无论吸积体是中子星、白矮星，还是像天鹅座X-1那样的黑洞。吸积盘是宇宙中最奇特的物体之一，除了专业天文学家之外，几乎没有人听说过它们。
Every X-ray binary has an accretion disk orbiting the accretor, be it a neutron star, a white dwarf or, as in Cyg X-1, a black hole. Accretion disks are among the most extraordinary objects in the universe, and almost no one except professional astronomers has ever even heard of them.
所有黑洞X射线双星系统周围都有吸积盘。甚至许多星系中心的超大质量黑洞周围也有吸积盘，但事实证明，我们银河系中心的超大质量黑洞周围可能并没有吸积盘。
There are accretion disks around all black hole X-ray binaries. There are even accretion disks orbiting supermassive black holes at the center of many galaxies, though probably not, as it turns out, around the supermassive black hole at the center of our own galaxy.
对吸积盘的研究如今已成为天体物理学的一个完整领域。您可以在这里看到一些精彩的吸积盘图像：www.google.com/images ?hl=en&q=xray+binaries&um=1&ie=UTF。关于吸积，还有很多内容值得探讨。我们对吸积盘知之甚少。最令人尴尬的问题之一是，我们仍然不甚了解吸积盘中的物质是如何到达致密天体的。另一个悬而未决的问题是，我们对吸积盘中的不稳定性缺乏了解，而这种不稳定性会导致物质流向致密天体的变化，以及X射线光度的变化。我们对一些X射线双星中存在的射电喷流的了解也十分有限。
The study of accretion disks is now an entire field of astrophysics. You can see some wonderful images of them here: www.google.com/images?hl=en&q=xray+binaries&um=1&ie=UTF. There is still lots about accretion disks that we don’t know. One of the most embarrassing problems is that we still don’t understand well how the matter in the accretion disks finds its way to the compact object. Another remaining problem is our lack of understanding of instabilities in the accretion disks, which give rise to variability in the matter flow onto the compact object, and the variability in X-ray luminosity. Our understanding of radio jets present in several X-ray binaries is also very poor.
一颗供体恒星每秒最多可以向吸积中子星输送约10¹⁸克物质。这听起来很多，但即使以这样的速度，也需要两百年才能输送相当于地球质量的物质。吸积盘中的物质在强大的引力场作用下流向吸积星，被加速到极高的速度：大约是光速的三分之一到二分之一。这些物质释放的引力势能转化为动能（大约5 × 10³⁰瓦），并将高速运动的氢气加热到数百万度的温度。
A donor star can transfer up to about 1018 grams per second to the accreting neutron star. It sounds like a lot, but even at that rate it would take two hundred years to transfer an amount of matter equal to the Earth’s mass. Matter from the disk flows toward the accretor in the grip of its intense gravitational field, which accelerates the gas to an extremely high speed: about one third to one half the speed of light. Gravitational potential energy released by this matter is converted into kinetic energy (roughly 5 × 1030 watts) and heats the racing hydrogen gas to a temperature of millions of degrees.
你知道，物质受热时会发出黑体辐射（参见第14章）。温度越高，辐射能量越大，波长越短，频率越高。当物质温度达到1000万至1亿开尔文时，它产生的辐射主要以X射线的形式存在。几乎全部5×10³⁰瓦的能量都以X射线的形式释放出来；相比之下，太阳的总光度（4×10²⁶瓦）中只有约10²⁰瓦是以X射线形式存在的。因此，太阳的表面温度与此相比简直就像一块冰。
You know that when matter is heated it gives off blackbody radiation (see chapter 14). The higher the temperature, the more energetic the radiation, making shorter wavelengths and higher frequencies. When matter reaches 10 to 100 million kelvin, the radiation it generates is mostly in X-rays. Almost all 5 × 1030 watts are released in the form of X-rays; compare that with the total luminosity of our Sun (4 × 1026 watts) of which only about 1020 watts is in the form of X-rays. Our Sun’s surface temperature is a veritable ice cube in comparison.
中子星本身太小，无法用光学望远镜直接观测到——但我们可以用光学望远镜观测到体积大得多的供体恒星和吸积盘。吸积盘本身会辐射出相当多的光，部分原因是由于一种叫做X射线加热的过程。当吸积盘中的物质撞击到中子星表面时，产生的X射线会向四面八方传播，从而也会撞击到吸积盘本身，使其温度进一步升高。我将在下一章关于X射线暴的内容中详细讲解这一点。
The neutron stars themselves are much too small to be seen optically—but we can see the much larger donor stars and the accretion disks with optical telescopes. The disks themselves can radiate quite a bit of light partly due to a process called X-ray heating. When the matter from the disk crashes onto the surface of the neutron star, the resultant X-rays go off in all directions and thus also slam into the disk itself, heating it to even higher temperatures. I will tell you more about that in the next chapter, on X-ray bursts.
X射线双星的发现解开了系外X射线辐射的第一个谜团。我们现在明白了为什么像天蝎座X-1这样的X射线源的X射线光度是其光学光度的1万倍。X射线来自温度高达数千万开尔文的极热中子星，而光学光则来自温度低得多的供体恒星和吸积盘。
The discovery of X-ray binaries solved the first mystery of extrasolar X-rays. We now understand why the X-ray luminosity of a source like Sco X-1 is ten thousand times greater than its optical luminosity. The X-rays come from the very hot neutron star (with temperatures of tens of millions kelvin), and the optical light comes from the much cooler donor star and the accretion disk.
当我们以为已经对X射线双星的运行机制有了相当深入的了解时，大自然又给我们带来了新的惊喜。X射线天文学家开始取得一些观测发现，这些发现远远超出了理论模型的预测。
When we thought that we had a fair understanding of how X-ray binaries work, nature had another surprise in store for us. The X-ray astronomers began making observational discoveries that were outstripping the theoretical models.
1975年，一项真正奇异的发现使我的科学生涯达到了一个高峰。我全身心地投入到观察、研究和解释这些非凡而神秘的现象——X射线暴——的工作中。
In 1975, the discovery of something truly bizarre led to a high point of my scientific career. I became completely immersed in the effort to observe, study, and explain these remarkable and mysterious phenomena: X-ray bursts.
关于X射线暴的故事，其中一部分包括我与俄罗斯科学家的争论，他们完全误解了数据；还有我与哈佛大学一些同事的争论，他们认为X射线暴是由质量巨大的黑洞产生的（可怜的黑洞，它们被冤枉了太多）。信不信由你，我甚至不止一次被要求以国家安全为由，不要发表一些关于X射线暴的数据。
Part of the story about X-ray bursts includes a battle I had with Russian scientists who completely misinterpreted their data and also with some of my colleagues at Harvard who believed that X-ray bursts were produced by very massive black holes (poor black holes, they have been unjustly blamed for so much). Believe it or not, I was even called (more than once) to not publish some data on bursts for reasons of national security.
第十四章
CHAPTER 14
X射线爆发！
X-ray Bursters!
大自然总是充满惊喜，1975年，它震撼了X射线界。事态发展如此激烈，以至于情绪有时都失控了，而我恰好身处其中。多年来，我一直与我在哈佛的一位同事争论不休（他根本不听我的意见），但我与我的俄罗斯同事交流得更顺利（他们愿意倾听）。由于我在这一切中扮演了核心角色，我可能很难保持客观，但我会尽力而为！
Nature is always full of surprises, and in 1975 it rocked the X-ray community. Things became so intense that emotions at times got out of control, and I was in the middle of it all. For years I was arguing with a colleague of mine at Harvard (who would not listen), but I had more luck with my Russian colleagues (who did listen). Because of my central role in all of this it may be very difficult for me to be objective, but I’ll try!
当时的新现象是X射线暴。1975年，格林德利和海斯利用荷兰天文卫星（ANS）的数据独立发现了X射线暴，而贝利安、康纳和埃文斯则利用美国两颗用于探测核试验的Vela-5间谍卫星的数据发现了X射线暴。X射线暴与我们之前在天蝎座X-1卫星上发现的亮度变化截然不同。天蝎座X-1的亮度变化在十分钟内增强了四倍，持续时间长达数十分钟。而X射线暴速度更快、亮度更高，持续时间却只有几十秒。
The new thing was X-ray bursts. They were discovered independently in 1975 by Grindlay and Heise using data from the Astronomical Netherlands Satellite (ANS) and by Belian, Conner, and Evans, using data from the United States’ two Vela-5 spy satellites designed to detect nuclear tests. X-ray bursts were a completely different animal from the variability we discovered from Sco X-1, which had a flare-up by a factor of four over a ten-minute period that lasted tens of minutes. X-ray bursts were much faster, much brighter, and they lasted only tens of seconds.
在麻省理工学院，我们拥有自己的卫星（于1975年5月发射），名为第三小型天文卫星，简称SAS-3。它的名字不如“乌呼鲁”那么浪漫，但这项工作却是我一生中最投入的。我听说过X射线暴，于是在1976年1月开始寻找它们；到3月，我们已经发现了5个。到年底，我们总共发现了10个。由于SAS-3的灵敏度以及它的配置方式，它成为了发现和研究X射线暴源的理想仪器。当然，它并非专门为探测X射线暴而设计的；所以从某种程度上来说，这有点运气成分。你看，幸运女神在我的人生中扮演了多么重要的角色！我们获得了惊人的数据——每天24小时，就像有金子从天而降——我日夜不停地工作。我全身心投入，甚至可以说是痴迷。能够拥有一个可以指向任何方向并获得高质量数据的X射线天文台，这真是一生难得的机会。
At MIT we had our own satellite (launched in May 1975) known as the Third Small Astronomy Satellite, or SAS-3. Its name wasn’t as romantic as “Uhuru,” but the work was the most absorbing of my entire life. We had heard about bursters and began looking for them in January 1976; by March we’d found five of our own. By the end of the year we’d found a total of ten. Because of the sensitivity of SAS-3, and the way it was configured, it turned out to be the ideal instrument to discover burst sources and to study them. Of course, it wasn’t specially designed to detect X-ray bursts; so in a way it was a bit of luck. You see what a leading role Lady Luck has played in my life! We were getting amazing data—a bit of gold pouring out of the sky every day, twenty-four hours a day—and I worked around the clock. I was dedicated, but also obsessed. It was a once in a lifetime opportunity to have an X-ray observatory you can point in any direction you want to and get data of high quality.
事实上，我们所有人都感染了“爆发热”——本科生、研究生、后勤人员、博士后和教职工——我至今仍能回忆起那种感觉，就像被光芒笼罩。我们最终被分到了不同的观测小组，这意味着我们之间，甚至彼此之间，都产生了竞争。有些人不喜欢这样，但我必须说，我认为这促使我们做得更多更好，而最终的科研成果也确实令人惊叹。
The truth is that we all caught “burst fever”—undergraduates and graduate students, support staff and postdocs and faculty—and I can still remember the feeling, like a glow. We ended up in different observing groups, which meant that we got competitive, even with one another. Some of us didn’t like that, but I have to say that I think it pushed us to do more and better, and the scientific results were just fantastic.
那种程度的痴迷对我的婚姻和家庭生活都极为不利。我的科研生涯的确得到了极大的提升，但我的第一次婚姻却因此破裂。当然，这都是我的错。多年来，我经常一走就是几个月，驾驶热气球环游半个地球。现在我们有了自己的卫星，我感觉自己还不如待在澳大利亚呢。
That level of obsession was not good for my marriage, and not good for my family life either. My scientific life was immeasurably enhanced, but my first marriage dissolved. Of course it was my fault. For years I’d been going away for months at a time to fly balloons halfway around the globe. Now that we had our own satellite, I might as well still have been in Australia.
这些突发事件源就像我们的家人一样。毕竟，我们与它们朝夕相处，对它们了如指掌。就像朋友一样，每个突发事件源都独一无二，有着各自的特点。即使现在，我仍然能认出许多这些典型的突发事件特征。
The burst sources became a kind of substitute family. After all, we lived with them and slept with them and learned them inside out. Like friends, each one was unique, with its own idiosyncrasies. Even now, I recognize many of these telltale burst profiles.
这些辐射源大多距离地球约25000光年，由此我们可以计算出，一次爆发（不到一分钟内发射）的总X射线能量约为10³²焦耳，这是一个几乎难以想象的数字。不妨这样理解：我们的太阳大约需要三天时间才能在所有波长范围内发射出10³²焦耳的能量。
Most of these sources were about 25,000 light-years away, which allowed us to calculate that the total X-ray energy in a burst (emitted in less than a minute) was about 1032 joules, a number that’s almost impossible to grasp. So look at it this way: it takes our Sun about three days to emit 1032 joules of energy in all wavelengths.
有些爆发几乎像钟表一样规律，例如：MXB 1659-29 的爆发周期约为 2.4 小时，而其他一些天体的爆发周期则从数小时变为数天，还有一些天体甚至几个月都没有爆发。MXB 中的 M 代表麻省理工学院 (MIT)，X 代表 X 射线，B 代表爆发源。这些数字表示天体在赤道坐标系中的天体坐标。对于业余天文爱好者来说，这些坐标应该很熟悉。
Some of these bursts came with nearly clocklike regularity, such as the bursts from MXB 1659-29, which produced bursts at 2.4-hour intervals, while others changed their burst intervals from hours to days, and some showed no bursts at all for several months. The M in MXB stands for MIT, the X for X-rays, and the B for burster. The numbers indicate the source’s celestial coordinates in what’s known as the equatorial coordinate system. For the amateur astronomers among you, this will be familiar.
当然，关键问题是这些爆发是由什么引起的？我在哈佛的两位同事（包括X射线爆发的共同发现者之一乔什·格林德利）在1976年提出了一种过于乐观的观点，认为这些爆发是由质量大于太阳数百倍的黑洞产生的。
The key question, of course, was what caused these bursts? Two of my colleagues at Harvard (including Josh Grindlay, who was one of the codiscoverers of X-ray bursts) got carried away and proposed in 1976 that the bursts were produced by black holes with a mass greater than several hundred times the mass of the Sun.
我们很快发现，X射线暴期间的光谱与冷却黑体的光谱非常相似。黑体并非黑洞，而是一个理想的模型，用来代表那些吸收所有入射辐射而不反射任何辐射的物体。（众所周知，黑色吸收辐射，白色反射辐射——这就是为什么在迈阿密的夏天，停在海滩停车场里的黑色汽车内部温度总是比白色汽车高。）理想黑体的另一个特点是，由于它不反射任何辐射，它唯一能发出的辐射就是自身温度产生的辐射。想想电炉里的加热元件。当它达到烹饪温度时，会开始发出红光，发出低频红光。随着温度升高，它会变成橙色，然后是黄色，通常不会再有太大变化。当断电时，元件冷却下来，它发出的辐射的轮廓或多或少类似于X射线暴的尾部。黑体的光谱非常容易研究，因此，如果你测量一段时间内的光谱，就可以计算出它冷却时的温度。
We soon discovered that the spectra during X-ray bursts resemble the spectra from a cooling black body. A black body is not a black hole. It’s an ideal construct to stand in for an object that absorbs all the radiation that strikes it, rather than reflecting any of it. (As you know, black absorbs radiation, while white reflects it—which is why in summer in Miami a black car left in a beach parking lot will always be hotter inside than a white one.) The other thing about an ideal black body is that since it reflects nothing, the only radiation it can emit is the result of its own temperature. Think about a heating element in an electric stove. When it reaches a cooking temperature, it begins to glow red, emitting low-frequency red light. As it gets hotter it reaches orange, then yellow, and usually not much more. When you turn off the electricity, the element cools, and the radiation it emits has a profile more or less like the tail end of bursts. The spectra of black bodies are so well known that if you measure the spectrum over time, you can calculate the temperature as it cools.
由于我们对黑体辐射的了解非常透彻，我们可以基于基础物理学推断出很多关于爆发的信息，这真是令人惊叹。我们当时正在分析25000光年外未知源的X射线发射光谱，而我们取得的突破性进展，竟然是用麻省理工学院一年级学生所学的物理学知识！
Since black bodies are very well understood, we can deduce a great deal about bursts based on elementary physics, which is quite amazing. Here we were, analyzing X-ray emission spectra of unknown sources 25,000 light-years away, and we made breakthroughs using the same physics that first-year college students learn at MIT!
我们知道，黑体的总光度（即它每秒辐射的能量）与其温度的四次方成正比。（这绝非直观），而且它与球体的表面积成正比（这很直观——面积越大，散发的能量就越多）。因此，如果我们有两个直径为一米的球体，其中一个的温度是另一个的两倍，那么温度较高的球体每秒散发的能量将是另一个的十六倍（2⁴ ）。由于球体的表面积与其半径的平方成正比，我们也知道，如果一个物体的温度保持不变，但体积增大到原来的三倍，那么它每秒散发的能量将是原来的九倍。
We know that the total luminosity of a black body (how much energy per second it radiates) is proportional to the fourth power of its temperature (this is by no means intuitive), and it is proportional to its surface area (that’s intuitive—the larger the area, the more energy can get out). So, if we have two spheres a meter in diameter, and one is twice as hot as the other, the hotter one will emit sixteen times (24) more energy per second. Since the surface area of a sphere is proportional to the square of its radius, we also know that if an object’s temperature stays the same but triples in size, it will emit nine times more energy per second.
在X射线爆发的任何时刻，X射线光谱都能告诉我们辐射源的黑体温度。爆发期间，温度会迅速上升到约3000万开尔文，之后缓慢下降。由于我们知道这些爆发源的大致距离，因此我们也可以计算出爆发期间任何时刻辐射源的亮度。一旦知道了黑体温度和亮度，就可以计算出辐射源的半径，而且在爆发期间的任何时刻都可以进行计算。第一个完成这项工作的人是美国宇航局戈达德太空飞行中心的吉恩·斯旺克；麻省理工学院的我们迅速跟进，并得出结论：这些爆发来自一个半径约为10公里的冷却天体。这有力地证明了爆发源是中子星，而不是质量巨大的黑洞。如果它们是中子星，那么它们很可能是X射线双星系统。
The X-ray spectrum at any moment in time of the burst tells us the blackbody temperature of the emitting object. During a burst, the temperature quickly rises to about 30 million kelvin and decreases slowly thereafter. But since we knew the approximate distance to these bursters, we could also calculate the luminosity of the source at any moment during the burst. But once you know both the blackbody temperature and the luminosity, you can calculate the radius of the emitting object, and that too can be done for any moment in time during the burst. The person who did this first was Jean Swank of NASA’s Goddard Space Flight Center; we at MIT followed quickly and concluded that the bursts came from a cooling object with a radius of about 10 kilometers. This was strong evidence that the burst sources were neutron stars, not very massive black holes. And if they were neutron stars, they were probably X-ray binaries.
1976年，意大利天文学家劳拉·马拉斯基（Laura Maraschi）访问麻省理工学院。二月的一天，她走进我的办公室，提出X射线暴是由热核闪光引起的，也就是吸积中子星表面发生的巨大热核爆炸。当氢吸积到中子星上时，引力势能会转化为极高的温度，从而释放出X射线（参见前一章）。马拉斯基认为，随着吸积物质在中子星表面不断积累，它可能会像氢弹爆炸一样发生失控的核聚变，从而引发X射线暴。几个小时后，当吸积了足够的核燃料时，下一次爆炸可能会发生。马拉斯基在我的黑板上用一个简单的计算证明，以大约半光速冲向中子星表面的物质会释放出更多的X射线。比热核爆炸释放的能量还要大，数据也证实了这一点。
The Italian astronomer Laura Maraschi was visiting MIT in 1976, and one day in February she walked into my office and suggested that the bursts were the result of thermonuclear flashes, huge thermonuclear explosions on the surface of accreting neutron stars. When hydrogen accretes onto a neutron star, gravitational potential energy is converted to such tremendous heat that X-rays are emitted (see previous chapter). But as this accreted matter accumulates on the surface of the neutron star, Maraschi suggested, it might undergo nuclear fusion in a runaway process (like in a hydrogen bomb) and that might cause an X-ray burst. The next explosion might go off a few hours later when enough new nuclear fuel had been accreted to ignite. Maraschi demonstrated with a simple calculation on my blackboard that matter racing at roughly half the speed of light to the surface of a neutron star releases much more energy than what is released during the thermonuclear explosions, and that is what the data showed.
我印象深刻——这个解释对我来说很有道理。热核爆炸完全符合条件。如果我们观测到的是中子星上的大爆炸，那么我们在爆发期间观察到的冷却模式也说得通。而且，她的模型很好地解释了爆发之间的间隔，因为爆炸所需的物质必须随着时间的推移而积累。按照正常的吸积速率，积累到临界质量应该需要几个小时，这与我们在许多爆发源中发现的间隔时间相符。
I was impressed—this explanation made sense to me. Thermonuclear explosions fit the bill. The cooling pattern we’d observed during the bursts also made sense if what we were seeing was a massive explosion on a neutron star. And her model explained the interval between bursts well since the amount of matter required for an explosion had to build up over time. At the normal rate of accretion, it should take a few hours to build up a critical mass, which was the kind of interval we found in many burst sources.
我在办公室里放着一台很奇特的收音机，总能让来访的客人感到不安。它里面装着太阳能电池，只有电池电量充足时才能工作。收音机放在那里吸收阳光，慢慢地充电（冬天充电更慢），然后大约每隔十分钟——如果天气糟糕，时间会更长——它就会突然开始播放，但只持续几秒钟，因为电量很快就耗尽了。你看，它电池的充电过程就像中子星上物质的积累：当积累到一定程度时，就会发生爆炸，然后逐渐消失。
I keep a funny kind of radio in my office that always unsettles visitors. It’s got a solar-powered battery inside, and it works only when the battery has enough juice. As the radio sits there soaking up sunlight, it slowly fills up with juice (a lot more slowly in the winter), then every ten minutes or so—sometimes longer if the weather’s rotten—it suddenly starts playing, but only for a couple of seconds, as it quickly exhausts its supply of electricity. You see? The buildup in its battery is just like the buildup of accreted matter on the neutron star: when it gets to the right amount, the explosion goes off, and then fades away.
随后，在马拉斯基来访几周后的1976年3月2日，正值爆发热潮之际，我们发现了一个X射线源，我将其命名为MXB 1730-335，它每天产生数千次爆发。这些爆发如同机关枪扫射一般——许多爆发之间仅间隔6秒！我不知道我是否能完全描述出当时我们对此感到多么匪夷所思。这个源（现在被称为快速爆发源）完全是个例外，它立刻否定了马拉斯基的想法。首先，中子星表面不可能在短短六秒内积累足够的核燃料来引发热核爆炸。不仅如此，如果这些爆发是吸积的副产品，我们应该观测到仅由吸积（引力势能的释放）产生的强X射线通量，远远超过爆发中蕴含的能量，但事实并非如此。因此，到了1976年3月初，马拉希关于核爆的精彩热核模型似乎已经彻底失效了。在我们的出版物中对于 MXB 1730-335，我们提出其爆发是由中子星上的“痉挛性吸积”引起的。换句话说，在大多数 X 射线双星中，热物质会从吸积盘稳定地流向中子星，但在快速爆发星中，这种吸积过程却非常不规则。
Then, several weeks after Maraschi’s visit, on March 2, 1976, in the middle of burst fever, we discovered an X-ray source that I named MXB 1730-335 that was producing a few thousand bursts per day. The bursts came like machine-gun fire—many were only 6 seconds apart! I don’t know if I can completely convey just how bizarre this seemed to us. This source (now called the Rapid Burster) was a complete outlier, and it immediately killed Maraschi’s idea. First, there is no way that a sufficient amount of nuclear fuel could build up in six seconds on the surface of a neutron star to produce a thermonuclear explosion. Not only that, but if the bursts were a by-product of accretion, we should see a strong X-ray flux due to accretion alone (release of gravitational potential energy), far exceeding the energy present in the bursts, but that was not the case. So it seemed in early March 1976 that Maraschi’s wonderful thermonuclear model for the bursts was as dead as the proverbial doornail. In our publication on MXB 1730-335, we suggested that the bursts are caused by “spasmodic accretion” onto a neutron star. In other words, what in most X-ray binaries is a steady flow of hot matter from the accretion disk onto the neutron star is very irregular in the case of the Rapid Burster.
当我们测量脉冲随时间的变化时，我们发现脉冲越大，下一次脉冲之间的等待时间就越长。下一次脉冲的等待时间最短可至六秒，最长可至八分钟。闪电也遵循类似的规律。当出现特别强烈的闪电时，由于放电量巨大，电场需要更长时间才能积蓄足够的电势，从而再次放电。
When we measured the bursts over time, we found that the bigger the burst, the longer the wait before the next one. The waiting time to the next burst could be as short as six seconds and as long as eight minutes. Lightning does something similar. When there’s a particularly large lightning bolt, the large discharge means that the wait needs to be longer for the electric field to build up its potential to the point that it can discharge again.
那年晚些时候，一篇1975年发表的关于X射线暴的俄文论文的译文突然出现；该论文报告了1971年利用“宇宙428”号卫星探测到的X射线暴。我们震惊了；苏联人发现了X射线暴，而且他们抢先一步，击败了西方！然而，随着我对这些X射线暴了解得越来越多，我开始变得非常怀疑。他们的X射线暴与我用SAS-3探测到的许多X射线暴的表现截然不同，这让我开始严重怀疑苏联的X射线暴是否真实存在。我怀疑它们要么是人为制造的，要么是以某种奇异的方式在地球附近产生的。铁幕使得追查真相变得困难重重；根本无从得知。不过，我有幸受邀参加了1977年夏天在苏联举行的一次高级别会议。只有12位苏联天体物理学家和12位美国天体物理学家受邀参加。正是在那里，我第一次见到了世界著名科学家约瑟夫·什克洛夫斯基、罗尔德·萨格杰耶夫、雅科夫·泽尔多维奇和拉希德·苏尼亚耶夫。
Later that year a translation of a 1975 Russian paper about X-ray bursts surfaced out of nowhere; it had been reporting burst detections made in 1971 with the Kosmos 428 satellite. We were stunned; the Russians had discovered X-ray bursts, and they had beaten the West! However, as I heard more and more about these bursts, I became very skeptical. Their bursts behaved so very, very differently from the many bursts that I had detected with SAS-3 that I began to seriously doubt whether the Russian bursts were real. I suspected that they were either man-made or produced near Earth in some odd, bizarre way. The iron curtain made it difficult to pursue this; there was no way to find out. However, I had the good fortune to be invited to attend a high-level conference in the Soviet Union in the summer of 1977. Only twelve Russians and twelve U.S. astrophysicists had been invited. That’s where I met for the first time the world famous scientists Joseph Shklovsky, Roald Sagdeev, Yakov Zel’dovich, and Rashid Sunyaev.
我做了一场关于X射线暴的演讲——你猜对了——并因此结识了那篇俄罗斯X射线暴论文的作者们。他们慷慨地向我展示了许多X射线暴的数据，远远超过他们在1975年发表的数据。我立刻意识到这一切都是无稽之谈，但我并没有告诉他们，至少一开始没有。我先去见了他们的上司，罗尔德·萨格杰耶夫，他当时是苏联科学院空间研究所的所长，该研究所位于莫斯科。我告诉他，我想和他讨论一些比较敏感的事情。他建议我们不要在他的办公室里谈（因为那里到处都是窃听器），所以我们去了外面。我把……我解释了为什么他们看到的X射线爆发并非他们所想的那样——他立刻就明白了。我告诉他，我担心如果我把这件事告诉全世界，可能会让这些人在苏联政权下惹上大麻烦。他向我保证不会这样，并鼓励我去见见他们，把我告诉他的原话告诉他们。于是我去了，那也是我们最后一次听到关于俄罗斯X射线爆发的消息。我还想补充一点，我们现在仍然是朋友！
I gave a talk on—you guessed it—X-ray bursts, and I got to meet the authors of the Russian burst paper. They generously showed me data of many bursts, way more than they had published in 1975. It was immediately obvious to me that all this was nonsense, but I did not tell them that, at least not at first. I first went to see their boss, Roald Sagdeev, who at the time was the director of the Space Research Institute of the USSR Academy of Sciences in Moscow. I told him that I wanted to discuss something rather delicate with him. He suggested we not do that in his office (bugs were all over the place), so we went outside. I gave him my reasons why their bursts were not what they thought they were—he immediately understood. I told him that I was afraid that my telling the world about this might get these guys into deep trouble under the Soviet regime. He assured me that that would not be the case, and he encouraged me to meet with them and tell them exactly what I had told him. So I did, and that was the last we ever heard of the Russian X-ray bursts. I’d like to add that we are still friends!
你可能很好奇这些俄罗斯爆炸声是怎么回事。当时我一无所知，但现在我知道了；它们是人为造成的，你猜是谁造成的——俄罗斯人！我稍后会解开这个谜团。
You may be curious to know what caused these Russian bursts. At the time I had no idea, but now I know; they were man-made, and guess who made them—the Russians! I’ll solve this mystery in a bit.
现在让我们回到真正的X射线暴，我们仍在努力研究它们。当X射线暴的X射线射入X射线双星的吸积盘（或供体星）时，吸积盘和供体星的温度会升高，并在可见光波段短暂发光。由于X射线必须先到达吸积盘和供体星，我们预期来自吸积盘的任何可见光闪光都会在X射线暴发生几秒钟后到达我们这里。因此，我们开始寻找同步发生的X射线和可见光暴。我的前研究生杰夫·麦克林托克（Jeff McClintock）和他的同事在1977年首次识别出了两个X射线暴源（MXB 1636-53和MXB 1735-44）。这两个源成为了我们的观测目标。
For now let’s return to the real X-ray bursts, which we were still trying to figure out. When the X-rays of the bursts plow into the accretion disk (or into the donor star) of an X-ray binary, the disk and the star get hotter and light up briefly in the optical part of the spectrum. Since the X-rays would first have to travel to the disk and donor star, we expected that any optical flash from the disk would reach us seconds after the X-ray burst. So we went hunting for coordinated X-ray and optical bursts. My former graduate student Jeff McClintock and his co-workers had made the first two optical identifications of burst sources (MXB 1636-53 and MXB 1735-44) in 1977. These two sources became our targets.
你明白科学是如何运作的吗？如果一个模型是正确的，那么它就应该产生可观察的结果。1977年夏天，我和我的同事兼朋友杰弗里·霍夫曼组织了一次全球同步的X射线、射电、光学和红外线“爆发监测”。
You see how science works? If a model is correct, then it ought to have observable consequences. In the summer of 1977 my colleague and friend Jeffrey Hoffman and I organized a worldwide simultaneous X-ray, radio, optical, and infrared “burst watch.”
这本身就是一次令人惊叹的冒险。我们必须说服来自十四个国家四十四个天文台的天文学家，在最有利的观测时段（被称为“暗夜”，即月光消失的时段）抽出宝贵的观测时间，凝视一颗可能毫无动静的暗星。他们愿意参与，足以说明天文学家对X射线暴之谜的重视程度。在三十五天的时间里，我们利用SAS-3探测到了来自X射线暴源MXB 1636-53的120次X射线暴，但地面望远镜却一次也没观测到。真是令人失望！
This was an amazing adventure all by itself. We had to convince astronomers at forty-four observatories in fourteen countries to devote precious observing time during the most favorable hours (known as “dark time,” when the Moon is absent) staring at one faint star—that might do nothing. That they were willing to participate shows you just how significant astronomers considered the mystery of X-ray bursts. Over thirty-five days, with SAS-3, we detected 120 X-ray bursts from the burst source MXB 1636-53 but absolutely no bursts were observed with the telescopes on the ground. What a disappointment!
你或许会以为我们需要向世界各地的同行道歉，但事实是，他们都没有觉得这是个问题。这就是科学的本质。
You might imagine that we had to apologize to our colleagues around the world, but the truth is that none saw it as a problem. This is what science is all about.
因此，第二年我们再次尝试，只使用大型地面望远镜。杰夫·霍夫曼已经前往休斯顿成为一名宇航员，但我的研究生林恩·科明斯基和荷兰天文学家扬·范·帕拉迪斯（他于 1977 年 9 月来到麻省理工学院）与我一起参加了 1978 年的爆发观测。*这次我们选择了MXB 1735–44。1978年6月2日晚，我们成功了！就在我们麻省理工学院用SAS-3探测到X射线暴几秒钟后，乔什·格林德利和他的同事们（包括麦克林托克）用位于智利托洛洛山的1.5米望远镜探测到了一次光学暴。我们的研究成果登上了《自然》杂志的头版，这真是莫大的荣幸。这项工作进一步巩固了我们关于X射线暴来自X射线双星的信念。
So we tried again the following year using only large ground-based telescopes. Jeff Hoffman had left for Houston to become an astronaut, but my graduate student Lynn Cominsky and the Dutch astronomer Jan van Paradijs (who had come to MIT in September 1977) joined me in the 1978 burst watch.* This time we selected MXB 1735–44. On the night of June 2, 1978, we succeeded! Josh Grindlay and his co-workers (including McClintock) detected an optical burst with the 1.5-meter telescope at Cerro Tololo in Chile a few seconds after we, at MIT, detected an X-ray burst with SAS-3. We made it to the front page of Nature, which was quite an honor. This work further supported our conviction that X-ray bursts come from X-ray binaries.
令我们百思不得其解的是，除了一个之外，所有爆发源每天只产生寥寥几次爆发，而快速爆发源却截然不同。答案就藏在我职业生涯中最奇妙——也最令人费解——的发现之中。
What was very puzzling to us was why all burst sources except one produce only a handful of bursts in a day and why the Rapid Burster was so very different. The answer lay with the most wonderful—and most bewildering—discovery of my career.
快速脉冲星（Rapid Burster）属于瞬变源。Cen X-2 也是一个瞬变源（参见第 11 章）。然而，快速脉冲星属于周期性瞬变源。在 20 世纪 70 年代，它大约每六个月会爆发一次，但每次只持续几周，之后就会停止发射。
The Rapid Burster is what we call a transient. Cen X-2 is also a transient (see chapter 11). However, the Rapid Burster is what we call a recurrent transient. In the 1970s it became burst-active about every six months, but only for several weeks, after which it would go off the air.
在我们发现快速爆发源大约一年半之后，我们注意到它的爆发轮廓有一些特殊之处，这使得这个神秘的源子成为了X射线爆发源的罗塞塔石碑。1977年秋季，当快速爆发源再次活跃时，我的本科生赫尔曼·马歇尔仔细观察了X射线爆发轮廓，并在极快爆发中发现了一种不同类型的爆发，这种爆发出现的频率要低得多，大约每三到四个小时一次。这些我们最初称之为特殊爆发的现象，展现出与黑体辐射类似的冷却轮廓。许多其他爆发源的所有爆发都具有这种特征。换句话说，我们之前称之为特殊爆发的那些——我们很快将它们称为I型爆发，并将快速爆发称为II型爆发——或许根本就不是什么特殊爆发。II型爆发显然是间歇性吸积的结果——这一点毋庸置疑——但或许常见的I型爆发最终是由热核闪光引起的。稍后我会解释我们是如何得出这个结论的——请耐心听我说。
About a year and a half after we discovered the Rapid Burster, we noticed something about its burst profiles that transformed this mystery source into a Rosetta Stone of X-ray bursters. In the fall of 1977, when the Rapid Burster was active again, my undergraduate student Herman Marshall looked very closely at the X-ray burst profiles and discovered a different kind of burst among the very rapid bursts, one that came far less frequently, about every three or four hours. These special bursts, as we called them at first, exhibited the same black body–like cooling profile that characterized all the bursts from the many other burst sources. In other words, perhaps what we were calling special bursts—we soon called them Type I bursts, and gave the rapid bursts the designation Type II—weren’t so special at all. The Type II bursts were clearly the result of spasmodic accretion—there was never any doubt about that—but maybe the common Type I bursts were due to thermonuclear flashes after all. I’ll tell you shortly how we figured that out—just bear with me.
1978年秋，我在麻省理工学院的同事保罗·乔斯（Paul Joss）对中子星表面热核闪光的性质进行了一些细致的计算。他得出结论：积累的氢首先会平静地聚变成氦，但一旦氦达到临界质量、压力和温度，就会发生剧烈爆炸，产生热核闪光（即I型爆发）。由此，他预测稳定吸积过程中释放的X射线能量大约是热核爆发释放能量的百倍。换句话说，可利用的引力势能大约是可利用的核能的百倍。
In the fall of 1978 my colleague Paul Joss at MIT had made some careful calculations about the nature of thermonuclear flashes on the surface of neutron stars. He concluded that the accumulated hydrogen first quietly fuses to helium, but that the helium, once it reaches a critical mass, pressure, and temperature, can then violently explode and produce a thermonuclear flash (thus a Type I burst). This led to a prediction that the X-ray energy released in the steady accretion should be roughly a hundred times larger than the energy released in the thermonuclear bursts. In other words, the available gravitational potential energy was roughly a hundred times larger than the available nuclear energy.
图中展示了1977年秋季SAS-3探测器探测到的快速爆发源的X射线暴。线条的高度代表约一秒内探测到的X射线数量，横轴代表时间。每个子图显示了约300秒的数据。快速重复的II型爆发按顺序编号。每个子图中都可见一个“特殊爆发”，它们的编号各不相同。这些特殊爆发属于I型爆发（热核闪光）。此图出自Hoffman、Marshall和Lewin发表于1978年2月16日《自然》杂志的文章。
X-ray bursts from the Rapid Burster detected with SAS-3 in the fall of 1977. The height of the line represents the number of detected X-rays in about one second, while the horizontal axis represents time. each panel shows about 300 seconds of data. The rapidly repetitive Type II bursts are numbered sequentially. One “Special Burst” is visible in each panel; they have different numbers. They are the Type I bursts (thermonuclear flashes). This figure is from Hoffman, Marshall, and Lewin, nature, 16 Feb. 1978.
在1977年秋季为期五天半的观测中，我们测量了快速爆发源X射线辐射的总能量，发现II型爆发的能量大约是“特殊”I型爆发的120倍。这成了关键证据！那时我们就知道，快速爆发源是一个X射线双星系统，I型爆发是由吸积中子星表面的热核闪光造成的，而II型爆发则是由物质从供体星流向中子星时释放的引力势能造成的。这一点毋庸置疑；从那时起，我们知道所有I型爆发源都是中子星X射线双星系统。与此同时，我们也确凿地知道，黑洞不可能是这些爆发的源头。黑洞没有表面，因此它们无法产生热核闪光。
We measured the total amount of energy emitted in X-rays from the Rapid Burster during the five-and-a-half days of our fall 1977 observations, and we found that about 120 times more energy was emitted in the Type II bursts than in the “special” Type I bursts. That was the clincher! At that point we knew that the Rapid Burster was an X-ray binary and that Type I bursts were the result of thermonuclear flashes on the surface of an accreting neutron star and that the Type II bursts were the result of the release of gravitational potential energy of the matter flowing from the donor star to the neutron star. There simply was no doubt about this anymore; from that time on, we knew that all Type I burst sources were neutron star X-ray binaries. At the same time we knew conclusively that black holes could not be the source of the bursts. Black holes have no surface, so they cannot produce thermonuclear flashes.
尽管到了1978年，我们大多数人已经非常清楚爆发源是吸积中子星双星系统，但哈佛大学的格林德利仍然坚持认为爆发实际上是由超大质量黑洞产生的。他甚至在1978年发表了一篇论文，试图解释超大质量黑洞是如何产生爆发的。我早就说过，科学家们很容易对自己的理论产生感情。剑桥的《真实报》（The Real Paper）刊登了一篇题为《哈佛与麻省理工的决裂》的长篇报道，其中还配有我和格林德利的照片。
Even though it was already crystal clear to most of us by 1978 that burst sources were accreting neutron star binaries, Grindlay at Harvard continued to insist that the bursts were in fact produced by massive black holes. He even published a paper in 1978 in which he tried to explain how the bursts are produced by very massive black holes. I told you scientists can get emotionally attached to their theories. The Real Paper in Cambridge ran a long story, “Harvard and MIT at the Brink,” featuring pictures of Grindlay and me.
1981 年，我和我的丹麦朋友 Holger Pederson、Jan van Paradijs 发现了 MXB 1636–53 爆发源的 3.8 小时轨道周期，这为爆发源的双星性质提供了证据。然而，直到 1984 年，格林德利才最终承认这一点。
Evidence for the binary nature of burst sources came in 1981 when my Danish friend Holger Pederson, Jan van Paradijs, and I discovered the 3.8-hour orbital period of the burst source MXB 1636–53. Yet, it was not until 1984 that Grindlay finally conceded.
因此，正是最奇特的X射线源——快速爆发源——帮助证实了正常（I型）X射线暴的理论，而正常（I型）X射线暴本身也一直是个谜。讽刺的是，尽管快速爆发源解释了很多问题，但它本身仍然是个谜。对于观测者来说倒也无妨，但对于理论家来说，这仍然是个尴尬的难题。我们所能做的，在某种程度上也是我们迄今为止所能做的，就是提出“痉挛性吸积”的解释——我知道，这听起来像是你在异国度假时可能会遇到的现象。而事实是，这只是文字游戏，并非如此。物理学。不知何故，原本要落向中子星的物质会在吸积盘中暂时滞留，之后一团或一圈物质会从吸积盘中释放出来，喷射到中子星表面，并以脉冲形式释放引力势能。我们称这种释放为吸积盘不稳定性，但这仅仅是个术语；没有人知道它为什么会发生，又是如何发生的。
So it was the weirdest X-ray source, the Rapid Burster, that helped confirm the theory of normal (Type I) X-ray bursts, which had been mystifying in their own right. The irony is that for all it explained, the Rapid Burster has remained mostly a mystery. Not so much for observers, but for theoreticians it remains an embarrassment. The best we could do, and in some ways the best we’ve ever been able to do, is come up with the explanation of “spasmodic accretion”—I know, it sounds like something you could catch on an exotic vacation. And the truth is, it’s words, not physics. Somehow, the matter headed for the neutron star is temporarily held up in the disk before a blob or a ring of matter is released from the disk and spurts down to the surface of the star, releasing gravitational potential energy in bursts. We call this release a disk instability, but that too is just words; no one has a clue why and how it works.
坦白说，我们也不明白X射线源反复瞬态行为背后的机制。它们为什么会忽明忽暗，如此反复？我们一无所知。1977年，SAS-3的所有探测器开始同时探测到X射线爆发。这很奇怪，因为它们观测天空的方向完全不同。我们唯一能想到的合理解释是，极高能的伽马射线穿透了整个航天器（X射线无法做到这一点），并在其后留下了信号。由于所有探测器同时“触发”，我们根本无法确定这些伽马射线来自哪个方向。在几个月的时间里，我们观测到了几十次这样的爆发，之后它们就停止了。但13个月后，它们又出现了。麻省理工学院的科学家们对此束手无策。
Frankly, we also do not understand what the mechanism is behind the recurrent transient behavior of X-ray sources. Why do they turn on and off and on and off? We just don’t know. Once in 1977 we started to pick up bursts simultaneously in all of SAS-3’s detectors. This was bizarre, since they were viewing the sky in totally different directions. The only reasonable explanation we could come up with was that very-high-energy gamma rays were penetrating the entire spacecraft (something that X-rays cannot do) and leaving signals behind. Since all detectors “fired” at the same time, we had no clue what direction these gamma rays were coming from. After we had observed a few dozen of these episodes over a period of several months, they stopped. But thirteen months later they started up again. No one at MIT had a clue.
在我的本科生克里斯蒂安·特勒夫森的帮助下，我开始对这些爆发进行分类，我们甚至根据它们的特征将它们分为A、B和C类爆发。我把它们全部存储在一个名为“SHIT BURSTS”（糟糕的爆发）的文件中。
With the help of one of my undergraduate students, Christiane Tellefson, I started to catalog these bursts, and we even classified them as bursts A, B, and C, depending on their profiles. I stored them all in a file that I labeled SHIT BURSTS.
我记得当时给NASA的一些人（他们每年都会来我们这里）做报告，告诉他们我们关于X射线暴的最新激动人心的研究成果，并给他们展示了一些奇特的X射线暴。我解释了我为什么迟迟不愿发表；在我看来，这些X射线暴看起来不太可靠。然而，他们鼓励我不要拖延发表。于是，我和克里斯蒂安娜开始撰写论文。
I remember giving a presentation to some people from NASA (who would visit us yearly), telling them our latest exciting news on X-ray bursts and showing them some of these bizarre bursts. I explained my reluctance to publish; they just didn’t look kosher to me. However, they encouraged me not to delay publishing. So Christiane and I started to write a paper.
有一天，我突然接到以前学生鲍勃·斯嘉丽的电话，他当时在洛斯阿拉莫斯国家实验室做机密研究。他要求我不要发表这些奇怪的脉冲。我想要一个解释，但他不能告诉我原因。他让我提供一些这些脉冲出现的时间。事情确实发生了，我也照做了。两天后他又打来电话，这次他以国家安全为由，力劝我不要发表。我差点从椅子上摔下来。我立刻打电话给我的朋友弗朗西丝·科尔多瓦，她曾经和我一起在麻省理工学院工作，但当时也在洛斯阿拉莫斯国家实验室工作。我告诉她我和鲍勃的谈话内容，希望她能帮我弄明白是怎么回事。她肯定和鲍勃讨论过这件事，因为几天后她也打来电话，劝我不要发表。为了让我安心，她向我保证，这些爆发在天文上没有任何意义。总之，我没有发表。
Then one day, completely out of the blue, I received a call from my former student Bob Scarlett, who was doing classified research at the Los Alamos National Laboratory. He asked me not to publish these weird bursts. I wanted an explanation, but he was not allowed to tell me why. He asked me to give him some of the times that these bursts had occurred, which I did. Two days later he called again and this time he urged me not to publish for reasons of national security. I nearly fell off my chair. I immediately called my friend France Córdova, who had once worked with me at MIT but who at that time was also working in Los Alamos. I told her about my conversations with Bob and hoped that she could cast some light on what was going on. She must have discussed it with Bob, because a few days later she too called and urged me not to publish. To put my mind at rest, she assured me that these bursts were of zero astronomical interest. To make a long story short, I did not publish.
多年后我才知道真相：那些“乱七八糟的爆发”是由几颗俄罗斯卫星产生的，这些卫星使用核动力发电机供电，而这些发电机内部含有极强的放射源。每当SAS-3探测器靠近任何一颗俄罗斯卫星时，这些放射源就会释放伽马射线，照射到我们的探测器上。还记得1971年俄罗斯人探测到的那些奇怪的爆发吗？我现在几乎可以肯定，那些爆发也是俄罗斯自己的卫星造成的……真是讽刺！
Many years later I learned what had happened: the “shit bursts” had been produced by several Russian satellites that were powered by nuclear electrical generators, which contain extremely strong radioactive sources. Whenever SAS-3 came near any of the Russian satellites, they would shower our detectors with gamma rays emitted by the radioactive sources. Now, remember those weird bursts detected by the Russians back in 1971? I’m now quite certain these were also caused by the Russians’ own satellites… what irony!
从20世纪70年代末到1995年，我人生中的这段时期无比充实。当时，X射线天文学是观测天体物理学的前沿领域。我对X射线暴的研究将我的科研生涯推向了巅峰。我每年大概要在世界各地举办十几场学术报告会，足迹遍布东欧、西欧、澳大利亚、亚洲、拉丁美洲、中东以及美国各地。我受邀在许多国际天体物理学会议上发表演讲，并担任三本X射线天文学著作的主编，最后一本是2006年出版的《致密恒星X射线源》。那是一段令人兴奋、无比美好的时光。
This period of my life, beginning in the late 1970s and going through 1995, was incredibly intense. X-ray astronomy was the cutting edge of observational astrophysics then. My involvement with X-ray bursts pushed me to the pinnacle of my scientific career. I probably gave a dozen colloquia yearly all over the world, in Eastern and Western Europe, Australia, Asia, Latin America, the Middle East, and throughout the United States. I got invited to give talks at many international astrophysics conferences and was the chief editor of three books on X-ray astronomy, the last one, Compact Stellar X-ray Sources, in 2006. It was a heady, wonderful time.
然而，尽管我们取得了惊人的进展，但快速爆发器的奥秘依然难以解开。我相信总有一天会有人解开它。而他们也会面临同样令人困惑的问题。这就是我热爱物理学的原因。这也是为什么我一直珍藏着一张快速爆发器爆发曲线的巨幅海报。在我的麻省理工学院办公室里，它被醒目地展示着。无论是在大型强子对撞机，还是在哈勃超深空场的最远端，物理学家们都在获取越来越多的数据，并提出越来越多精妙绝伦的理论。我唯一确信的是，无论他们发现什么、提出什么、构建什么理论，都将揭开更多谜团。在物理学中，更多的答案往往会引出更多的问题。
And yet, despite the amazing advances we made, the Rapid Burster has resisted all attempts to unlock its deepest mysteries. Someone will figure it out some day, I’m sure. And they in turn will be confronted with something equally perplexing. That’s what I love about physics. And why I keep a poster-size reproduction of the Rapid Burster’s burst profiles prominently displayed in my MIT office. Whether it’s in the Large Hadron Collider or at the farthest reaches of the Hubble Ultra Deep Field, physicists are getting more and more data, and coming up with more and more ingenious theories. The one thing I know is whatever they find, and propose, and theorize, they’ll uncover yet more mysteries. In physics, more answers lead to even more questions.
第十五章
CHAPTER 15
看待事物的方式
Ways of Seeing
大多数高中生和大学生都讨厌物理，因为它通常被当作一套复杂的数学公式来教授。这并非我在麻省理工学院采用的方法，也不是我在这本书中采用的方法。我将物理呈现为一种观察世界的方式，它揭示了那些原本隐藏在我们视野之外的领域——从最小的亚原子粒子到浩瀚的宇宙。物理让我们能够看到周围无处不在的无形力量，从引力到电磁力，并让我们不仅能够发现彩虹，还能发现光晕、雾虹、光辉，甚至可能是玻璃虹。
Most high school and college students hate taking physics because it is usually taught as a complicated set of mathematical formulas. That is not the approach I use at MIT, and it is not the approach I use in this book. I present physics as a way of seeing our world, revealing territories that would otherwise be hidden to us—from the tiniest subatomic particles to the vastness of our universe. Physics allows us to see the invisible forces at play all around us, from gravity to electromagnetism, and to be on the alert not only for where and when we’ll find rainbows, but also halos, fogbows, and glories, and maybe even glassbows.
每一位物理学先驱都改变了我们看待世界的方式。牛顿之后，我们能够理解并预测整个太阳系的运动，而且我们拥有了实现这一目标所需的数学工具——微积分。牛顿之后，没有人能够否认阳光是由各种颜色组成的，也没有人能够否认彩虹是由阳光在雨滴中折射和反射形成的。麦克斯韦之后，电和磁从此密不可分：甚至在这本书中，我也很难将它们分开来写。
Each pioneering physicist changed the way we look at the world. After Newton, we could understand and predict the movements of the entire solar system, and we had the mathematics—calculus—to do so. After Newton, no one could claim that sunlight was not made up of colors, or that rainbows came from anything but sunlight refracting and reflecting in raindrops. After Maxwell, electricity and magnetism were forever linked: it was even hard for me to separate them into different chapters in this book.
这就是为什么我认为物理学和艺术之间存在着一种奇妙的联系；先锋艺术也是一种全新的视角，一种看待世界的新方式。你或许会惊讶地发现，我一生中大部分时间对现代艺术的痴迷程度几乎与我对物理学的痴迷程度不相上下；我对两者都充满热爱！我之前已经提到过我收藏的大量Fiestaware餐具。自六十年代中期以来，我还收藏了一百多件艺术品——绘画、拼贴画、雕塑、地毯、椅子、桌子、木偶、面具等等——如今我家里的墙面和地面空间已经不足以全部展示它们了。
This is why I see a fascinating relationship between physics and art; pioneering art is also a new way of seeing, a new way of looking at the world. You might be surprised to learn that for much of my life I’ve been almost as obsessed with modern art as I have been with physics; I have a love relationship with both! I’ve already mentioned my large collection of Fiestaware. I’ve also collected more than a hundred works of art—paintings, collages, sculptures, rugs, chairs, tables, puppets, masks—since the mid-sixties, and I no longer have enough wall or floor space in my home to display them all.
在麻省理工学院的办公室里，物理学占据主导地位，尽管我也收藏了两件学校借来的艺术佳作。但在家里，我大概只有十几本物理书，却有大约250本艺术书籍。我很幸运，从小就培养了对艺术的热爱。
In my office at MIT, physics dominates, though I have two great works of art on loan from the university. But at home I probably only have about a dozen physics books—and about 250 art books. I was fortunate in being initiated into a love of art early.
我的父母收藏艺术品，尽管他们对艺术的理论知识知之甚少。他们只是凭着喜好挑选，而这种做法有时会让他们误入歧途。有时他们挑选到一些伟大的作品，有时则不然，至少事后看来是这样。有一幅画给我留下了深刻的印象，那是我父亲的肖像，现在就挂在我剑桥的壁炉上方。它确实非常引人注目。我父亲是个很有个性的人——而且和我一样，他非常固执己见。那位非常了解他的画家，出色地捕捉到了他上半身的神韵：他硕大、光秃秃的长脸，坐落在他宽阔有力的方肩之间，小嘴上挂着一丝自鸣得意的微笑。但真正引人注目的是他的眼镜：厚厚的黑色镜框勾勒出他那双看不见的眼睛，仿佛在注视着你，而他的左眉则疑惑地挑了起来。这就是他全部的性格：一针见血。
My parents collected art, though they knew very little about it intellectually. They simply went by what they liked, which can lead down some blind alleys. Sometimes they picked some great works, and sometimes some not so great, or at least so it appears with the benefit of hindsight. One painting that made a strong impression on me is a portrait of my father, which I now have hanging over my fireplace in Cambridge. It is really very striking. My father was a real character—and like me, he was very opinionated. The artist, who knew him very well, caught him superbly, from the waist up, with his large, bald, oblong head sitting between his powerful square shoulders, his small mouth set in a self-satisfied smile. But it’s his glasses that truly stand out: thick, black, outlining invisible eyes, they follow you around the room, while his left eyebrow arches quizzically over the frame. That was his entire personality: penetrating.
我高中时，父亲经常带我去美术馆和博物馆，正是在那时，我真正开始爱上艺术，因为它教会了我新的欣赏方式。我喜欢美术馆和博物馆的一点是，与学校不同，你可以按照自己的兴趣来参观，想停就停，想待多久就待多久，想走就走。你可以建立起自己与艺术的独特联系。我很快就开始去……我独自一人逛博物馆，没过多久就积累了一些知识。我开始深入研究梵高。（你知道他的名字其实发音是“梵·乔奇”吗？如果你不是荷兰人，这几乎是无法发音的，两个喉音之间只隔着一个短促的“o”音。）十五岁那年，我给班上的同学讲了一堂关于梵高的课。我有时也会带朋友们去博物馆参观。所以，真正让我走上教书之路的，其实是艺术。
My father took me to art galleries and museums when I was in high school, and it was then that I really began to fall in love with art, as it taught me new ways of seeing. I loved that in galleries and museums, as opposed to school, you proceed according to your own interests, stopping when you wish, staying as long as you like, moving on when it suits you. You develop your own relationship to art. I soon started going to museums on my own, and before long, I had acquired a bit of knowledge. I plunged into van Gogh. (You know his name is really pronounced van Chocch—it’s all but unpronounceable if you’re not Dutch, two gutturals barely separated by a short O sound.) I ended up giving a lecture about van Gogh to my class when I was fifteen. I would also take my friends on tours to museums sometimes. So it was really art that got me into teaching.
正是在那时，我第一次体会到教导他人——无论年龄大小——拓展思维、探索新领域是多么美妙的感觉。艺术对很多人来说，就像物理学一样晦涩难懂，这实在令人惋惜，尤其是那些曾经遇到糟糕物理老师的人。正因如此，过去八年来，我每周都会在麻省理工学院的公告栏上发布一个艺术小测验——我会从网上打印一张图片，并提出问题：“这位艺术家是谁？”我会给一年中答对最多的三位参赛者颁发奖品——一些非常精美的艺术书籍。有些常客会花几个小时在网上搜索答案，在这个过程中，他们也学到了很多艺术知识！我非常享受每周的测验，所以现在我在我的Facebook主页上也设置了每两周一次的测验。如果你有兴趣，不妨也试试。
This is when I first learned what a wonderful feeling it is to teach others—of any age—to expand their minds into new realms. It’s a real shame that art can seem as obscure and difficult as so much of physics does to so many who had poor physics teachers. This is one reason that for the past eight years I’ve enjoyed putting an art quiz on my MIT bulletin board every week—an image I print off the web, with the question “Who is the artist?” I give prizes—some very nice art books—to the three contestants who have the most correct answers over the course of the year. Some regulars spend hours scouring the web and in doing so, they learn about art! I had so much fun with the weekly quiz that I’ve now put up a biweekly one on my Facebook page. You can try it yourself if you like.
我非常幸运，一生中曾有机会与一些杰出的、前卫的艺术家合作。20世纪60年代末，德国“天空艺术家”奥托·皮内来到麻省理工学院，担任高级视觉研究中心的研究员，后来又担任该中心主任长达二十年。那时我已经开始放飞一些巨型气球，所以有机会帮助奥托创作他的一些天空艺术作品。我们合作的第一个项目叫做“光线实验”，它由四根250英尺长的聚乙烯管组成，管内充满氦气。当管子的两端被固定住时，它们在麻省理工学院运动场的春风中划出优美的弧线。我们将这四根管子绑在一起，做成一个一千英尺长的气球，然后让一端升空。到了晚上，我们用聚光灯照亮这些蛇形气球的部分区域，它们在数百英尺的高空扭动、摇摆，呈现出令人惊叹、不断变化的形状。真是太棒了！
I’ve also been lucky enough to have had some wonderful chances to collaborate with some amazing, cutting-edge artists in my life. In the late 1960s the German “sky artist” Otto Piene came to MIT as a fellow at the Center for Advanced Visual Studies, and later ended up directing it for two decades. Because I had already been flying some of my giant balloons by then, I got to help Otto make some of his sky art. The very first project we worked on together was called the Light Line Experiment, and consisted of four 250-foot-long polyethylene tubes filled with helium that, when held down at each end, made elegant arcs in the spring breezes at the MIT athletic fields. We tied all four together to make a thousand-foot-long balloon and let one end float up into the sky. At night we brought out spotlights that lit up parts of the snakelike balloons as they twisted and waved in the most amazing, constantly changing shapes, hundreds of feet in the air. It was fabulous!
在这些项目中，我的工作通常是技术性的：弄清楚奥托提出的气球尺寸和形状的想法是否可行。例如，聚乙烯薄膜应该有多厚？我们希望它足够轻，能够升空，但又足够坚固，能够在有风的情况下保持直立。在1974年科罗拉多州阿斯彭举办的一次活动中，我们用系绳将多面玻璃珠悬挂在一个“光帐篷”上。我针对不同尺寸的气球和珠子的重量进行了大量的计算，以找到一个在物理和美学上都可行的解决方案。我喜欢用物理方法将奥托的艺术构想变为现实。
My job in these projects was usually technical: figuring out whether Otto’s ideas for the sizes and shapes of the balloons would be feasible. How thick should the polyethylene be, for example? We wanted it to be light enough to rise, but strong enough to stand up under windy conditions. At a 1974 event in Aspen, Colorado, we hung multifaceted glass beads from the tether lines of a “light tent.” I made many calculations regarding the different balloon sizes and bead weights in order to get to a workable solution in terms of physics and aesthetics. I loved doing the physics to make Otto’s artistic ideas a reality.
我深深地投入到他为1972年慕尼黑奥运会闭幕式设计的那只巨大的五色彩虹气球的项目中。当然，我们当时完全没有预料到那届奥运会会以以色列运动员惨遭屠杀而告终，因此，我们那只1500英尺长、在奥林匹克海面上空高出近500英尺的彩虹气球，成为了在灾难面前的希望象征。彩虹气球的照片可以在插图中看到。当我开始放飞气球探索宇宙时，我从未想过自己会参与到这样的项目中。
I got really involved with the immense, five-color Rainbow balloon he designed for the closing ceremonies of the 1972 Olympics in Munich. We of course had no idea that the Olympics would end so disastrously, with the massacre of the Israeli athletes, so our 1,500-foot Rainbow, which arched nearly five hundred feet high over the Olympic sea, became a symbol of hope in the face of catastrophe. A picture of the Rainbow balloon can be seen in the insert. When I began flying balloons to look at the universe, it never occurred to me that I could be involved in such projects.
奥托向我介绍了荷兰艺术家彼得·斯特鲁伊肯，我对他的作品并不陌生，因为我的父母在荷兰收藏了他的作品。有一天，奥托在麻省理工学院给我打电话说：“我办公室里来了一位荷兰艺术家，你想见见他吗？”人们总是想当然地认为，如果我们来自同一个小国，就应该会很乐意聊天，但通常情况下，我并不想。我问奥托：“我为什么要见他？他叫什么名字？”当奥托说出“彼得·斯特鲁伊肯”时，我当然同意了，但为了保险起见，我告诉奥托我只能见半个小时（其实我撒谎了）。于是彼得来到我的办公室；我们聊了将近五个小时（没错，五个小时！），之后我邀请他去Legal Sea Foods吃生蚝！我们一见如故，彼得也成了我二十多年的挚友。这次拜访彻底改变了我的人生！
Otto introduced me to the Dutch artist Peter Struycken, whose art I knew well because my parents had collected his works in the Netherlands. Otto called me up one day at MIT and said, “There’s this Dutch artist in my office; would you like to meet him?” People always assume that if we’re from the same little country we’d like to chat, but more often than not, I don’t want to. I told Otto, “Why should I, what’s his name?” When Otto said “Peter Struycken,” of course I agreed, but in order to play it safe, I told Otto that I could only meet for half an hour (which was not true). So Peter came over to my office; we talked for almost five hours (yes, five hours!) and I invited him for oysters at Legal Sea Foods afterward! We clicked right from the start, and Peter became one of my closest friends for more than twenty years. This visit changed my life forever!
在第一次谈话中，我成功地让彼得“明白”了他主要的问题/疑问——“什么时候某物与另一物有所不同”——的原因。还有什么区别呢？——这完全取决于你如何定义“区别”。对某些人来说，正方形可能不同于三角形，也不同于圆形。然而，如果你把自闭合的几何线段定义为相同的图形——那么，这三种图形就完全相同了。
During that first discussion I was able to make Peter “see” why his major problem/question—“When is something different from something else?”—all depends on one’s definition of difference. For some, a square may be different from a triangle and different from a circle. However, if you define geometric lines that close onto themselves as the same—well, then these three shapes are all the same.
彼得给我看了十几幅电脑绘图，都是用同一个软件画的，他说：“它们都一样。” 但在我看来，它们看起来却截然不同。这完全取决于你对“一样”的定义。我补充说，如果对他来说它们都一样，或许他愿意给我留一幅。他真的留了一幅，上面用荷兰语写着“Met dank voor een gesprek”（字面意思是“感谢讨论”）。这很符合彼得的风格：非常非常低调。坦白说，在我收藏的众多斯特鲁伊肯的作品中，这幅小画是我最喜欢的。
Peter showed me a dozen computer drawings, all made with the same program, and he said, “They are all the same.” To me they looked all very different. It all depends on one’s definition of “the same.” I added that if they were all the same to him, perhaps he would like to leave me one. He did and he wrote on it, in Dutch, “Met dank voor een gesprek” (literally, “With thanks for a discussion”). This was typical Peter: very very low key. Frankly, of the many Struyckens I have, this small drawing is my very favorite.
彼得发现我不仅是一位对艺术充满热情的物理学家，还能在他的工作中助他一臂之力。他是计算机艺术领域的先驱之一。1979年，彼得（与利恩和丹尼尔·德克斯一起）来到麻省理工学院待了一年，我们开始密切合作。我们几乎每天都见面，我每周去他家吃两三次饭。在认识彼得之前，我只是“观看”艺术——而彼得让我“领悟”了艺术。
Peter had found in me a physicist who was not only very interested in art, but who could help him with his work. He is one of the world’s pioneers in computer art. In 1979 Peter (with Lien and Daniel Dekkers) came for a year to MIT, and we started working together very closely. We met almost daily, and I had dinner at his place two or three times a week. Before Peter I “looked” at art—Peter made me “see” art.
如果没有他，我想我永远也不会学会关注开创性的作品，也不会明白它们如何从根本上改变我们看待世界的方式。我明白了艺术不仅仅是，甚至主要不是关于美；它关乎发现，而这正是艺术与物理学对我而言的交汇之处。
Without him, I think I never would have learned to focus on pioneering works, to see how they can fundamentally transform our ways of seeing the world. I learned that art is not only, or even mostly, about beauty; it is about discovery, and this is where art and physics come together for me.
从那时起，我对艺术的看法发生了彻底的改变。我“喜欢”什么不再重要，重要的是艺术的品质，是看待世界的新视角，而这只有真正了解艺术的人才能欣赏。我开始仔细研究作品的创作年份。马列维奇1915年至1920年间的开创性作品令人着迷。而其他艺术家在20世纪30年代创作的类似画作则让我提不起兴趣。“艺术要么是抄袭，要么是革命，”保罗·高更曾以他特有的傲慢语气说道，但其中也不乏真知灼见。
From that time on, I began to look at art very differently. What I “liked” was no longer important to me. What counted was the artistic quality, the new way of looking at the world, and that can only be appreciated if you really know something about art. I began to look closely at the years that works were made. Malevich’s pioneering works of art from 1915 to 1920 are fascinating. Similar paintings made by others in the 1930s are of no interest to me. “Art is either plagiarism or revolution,” said Paul Gauguin, with typical Gauguin arrogance, but there is some truth in it.
我被那些开创性作品的演变过程深深吸引。作为一名例如，我很快就能准确说出蒙德里安作品的创作年份——他在1900年至1925年间的艺术发展令人惊叹——现在我的女儿宝琳也能做到这一点了。多年来，我不止一次注意到博物馆有时会标错画作的创作日期。当我指出这一点时（我总是这样做），策展人有时会感到尴尬，但他们最终都会改正。
I was fascinated by the evolution that led to pioneering works. As an example, soon I was able to accurately tell the year that a Mondrian was made—his development between 1900 and 1925 was staggering—and my daughter Pauline can do that now too. Over the years I have noticed more than once that museums sometimes list the wrong date for a painting. When I point this out (as I always do), curators are sometimes embarrassed, but they always change it.
我曾与彼得合作过十几个项目。我们的第一个项目是“十六空间”，一个十六维空间的艺术创作（我们超越了拥有十一维空间的弦理论）。我还记得彼得的“移位”系列。他为一个计算机程序开发了数学基础，该程序可以生成非常复杂且有趣的艺术作品。但由于他数学水平不高，他的方程式非常怪异——简直荒谬。他想让数学变得优美，但却不知道该如何实现。
I worked with Peter on a dozen of his ideas. Our first project was “16th Space,” art in sixteen dimensions (we beat string theory with its eleven dimensions). I also recall Peter’s Shift series. He had developed a mathematical underpinning to a computer program that generated very complex and interesting art. But because he didn’t know much math, his equations were bizarre—really ridiculous. He wanted the math to be beautiful but didn’t know how to do it.
我想到一个解决方案，其实在物理学上并不复杂：三维行波。你可以设定波长，确定波速，还可以指定波的传播方向。如果你想要三个波相互交叉，也可以做到。你先设定一个初始条件，然后让这些波相互交叉传播，最后将它们叠加起来。这样就能产生非常有趣的干涉图样。
I was able to come up with a solution, not so complicated in physics at all: traveling waves in three dimensions. You can set the wavelength; you can determine the speed of the waves; and you can indicate their directions. And if you want three waves going through one another, you can do that. You start with a beginning condition and then you let the waves go through one another and add them up. This produces very interesting interference patterns.
背后的数学原理非常优美，这对彼得来说至关重要。我并非自夸——他也会这么说。我一生中扮演的主要角色就是：向他展示如何将数学表达得既优美又易于理解。他总是非常慷慨地让我从每个系列中挑选一件艺术品。我真是幸运，竟然收藏了大约十三件斯特鲁伊肯的作品！
The underlying math was beautiful, and that was very important for Peter. I don’t mean to boast—he would tell you the same thing. This is the role that I have mostly played in his life: to show him how to make things mathematically beautiful and easy to understand. He very kindly always let me choose one work of art from each series. Lucky me, I have about thirteen Struyckens!
由于我与彼得的合作，1979年，我受鹿特丹博伊曼斯·范·伯宁根博物馆馆长的邀请，在阿姆斯特丹科佩尔教堂巨大的穹顶下发表了首届蒙德里安讲座。当时教堂座无虚席，大约有九百名听众。这项极具声望的讲座如今每两年举办一次。1981年的演讲者是翁贝托·埃科，1993年是唐纳德·贾德，1995年是雷姆·库哈斯，2010年是查尔斯·詹克斯。
As a result of my collaboration with Peter, I was invited by the director of the Boijmans van Beuningen Museum in Rotterdam to give the first Mondrian Lecture in 1979 under the vast dome of Amsterdam’s Koepelkerk. It was packed; there were about nine hundred people in my audience. This very prestigious lecture is now given every other year. The lecturer in 1981 was Umberto Eco, Donald Judd in 1993, Rem Koolhaas in 1995, and Charles Jencks in 2010.
我与奥托和彼得的合作并非我参与艺术创作的唯一途径；我曾经（开玩笑地）尝试自己创作一些概念艺术作品。在我题为“以物理学家的视角看20世纪艺术”（http://mitworld.mit.edu/speaker/view/55）的讲座中，我解释说，我家里有大约十几本物理书籍，但艺术书籍至少有两百五十本，比例大约是二十比一。我把十本艺术书籍放在桌子上，邀请听众在中场休息时翻阅。为了保持适当的平衡，我宣布，我带来了半本物理书。那天早上，我把一本物理教材从书脊中间切开了。于是我举起那半本书，指着说我切得很小心——它真的只有半本书。“对于那些对艺术不感兴趣的人，”我一边说着，一边把书重重地摔在桌子上，“这就是给你们的！”恐怕没人明白。
My collaborations with Otto and Peter have not been my only involvement in making art; I once tried (in jest) to make a bit of conceptual art myself. When I gave my lecture “Looking at 20th-Century Art Through the Eyes of a Physicist” (http://mitworld.mit.edu/speaker/view/55), I explained that at home I have about a dozen books on physics but at least two hundred fifty on art, so the ratio is about twenty to one. I placed ten art books on the desk and invited the audience to look through them at the intermission. In order to keep the proper balance, I announced, I’d brought half a book on physics. That morning I had sliced a physics text in two, right down the middle of the spine. So I held it up, pointing out that I’d cut it very carefully—it was really half a book. “For those of you uninterested in art,” I said—dropping it loudly on the table—“here you are!” I’m afraid no one got it.
如果我们回顾文艺复兴时期至今的艺术发展历程，会发现一个清晰的趋势。艺术家们逐渐摆脱了既有传统的束缚：题材、形式、材料、透视、技法和色彩等方面的束缚。到了十九世纪末，艺术家们彻底摒弃了将艺术视为自然世界再现的观念。
If we look back at the days of Renaissance art up to the present, then there is a clear trend. The artists are gradually removing the constraints that were put on them by prevailing traditions: constraints of subject matter, of form, of materials, of perspective, of technique, and of color. By the end of the nineteenth century, artists completely abandoned the idea of art as a representation of the natural world.
事实上，我们现在认为这些开创性的作品非常精彩，但艺术家们的初衷却截然不同。他们想要引入一种全新的世界观。许多我们今天视为经典之作的杰作——例如梵高的《星夜》或马蒂斯的《绿条纹》（他妻子的肖像画）——在当时都曾遭受嘲笑和敌意。如今备受推崇的印象派画家——莫奈、德加、毕沙罗、雷诺阿——如今在各大博物馆中都享有盛名，但他们在开始展出作品时也曾面临嘲讽。
The truth is that we now find many of these pioneering works magnificent, but the intention of the artists was quite something else. They wanted to introduce a new way of looking at the world. Many of the works that we admire today as iconic and beautiful creations—van Gogh’s Starry Night, for example, or Matisse’s The Green Stripe (a portrait of his wife) received ridicule and hostility at the time. Today’s beloved Impressionists—Monet, Degas, Pissarro, Renoir—among the most popular artists in any museum today, also faced derision when they began showing their paintings.
我们大多数人现在都觉得他们的作品很美，这表明艺术家们战胜了他们所处的时代：他们看待世界的新方式，他们看待世界的新方式，已经成为了我们的世界，我们的世界观。一百年前丑陋的东西，如今可以被视为美。我喜欢一位当代评论家称马蒂斯为“丑陋的使徒”这个说法。收藏家利奥·斯坦称他收藏的马蒂斯夫人的画作《戴帽子的女人》是“我见过的最恶心的污点”——但他还是买下了这幅画！
The fact that most of us find their works beautiful now shows that the artists triumphed over their age: their new way of seeing, their new way of looking at the world, has become our world, our way of seeing. What was just plain ugly a hundred years ago can now be beautiful. I love the fact that a contemporary critic called Matisse the apostle of ugliness. The collector Leo Stein referred to his painting of Madame Matisse, Woman with a Hat, as “the nastiest smear I have ever seen”—but he bought the painting!
二十世纪的艺术家们使用现成物品——有时甚至是令人震惊的物品，例如马塞尔·杜尚的男用小便池（他称之为“喷泉”）和他创作的《蒙娜丽莎》，他在上面写下了挑衅性的字母 LHOOQ。杜尚是一位伟大的解放者；在杜尚之后，一切皆有可能！他想要彻底改变我们看待艺术的方式。
In the twentieth century artists used found objects—sometimes shocking ones, like Marcel Duchamp’s urinal (which he called “fountain”) and his Mona Lisa, on which he wrote the provocative letters L.H.O.O.Q. Duchamp was the great liberator; after Duchamp anything goes! He wanted to shake up the way we look at art.
在看过梵高、高更、马蒂斯和德兰的作品之后，没有人能再用同样的眼光看待色彩。同样，在看过安迪·沃霍尔的作品之后，也没有人能再用同样的眼光看待坎贝尔汤罐头或玛丽莲·梦露的照片。
No one can look at color in the same way after van Gogh, Gauguin, Matisse, and Derain. Nor can anyone look at a Campbell’s soup can or an image of Marilyn Monroe in the same way after Andy Warhol.
开创性的艺术作品可能很美，甚至令人惊艳，但大多数时候——至少在最初——它们令人费解，甚至可能很丑陋。一件开创性艺术作品的真正美，无论多么丑陋，都在于它的意义。看待世界的新方式从来不是熟悉的温暖床铺；它总是一场令人心旷神怡的冷水澡。我发现这场冷水澡令人精神焕发、精神振奋、获得解脱。
Pioneering works of art can be beautiful, even stunning, but most often—certainly at first—they are baffling, and may even be ugly. The real beauty of a pioneering work of art, no matter how ugly, is in its meaning. A new way of looking at the world is never the familiar warm bed; it’s always a chilling cold shower. I find that shower invigorating, bracing, liberating.
我对物理学领域的开创性工作也有同样的看法。一旦物理学又一次以令人惊叹的启示性步伐进入了以前不可见或晦涩的领域，我们就再也无法用同样的眼光看待世界了。
I think about pioneering work in physics in this same way. Once physics has taken another of its wonderfully revelatory steps into previously invisible or murky terrain, we can never see the world quite the same way again.
我在本书中介绍的诸多惊人发现，在当时都令人费解。如果要学习这些发现背后的数学原理，那将是一项艰巨的任务。但我希望，我对其中一些最重大突破的介绍，能够让读者真切感受到它们的精彩与美妙。正如塞尚、莫奈、梵高、毕加索、马蒂斯、蒙德里安、马列维奇、康定斯基、布朗库西、杜尚、波洛克和沃霍尔开辟了挑战艺术界的新道路一样，牛顿以及所有追随他的人们也为我们带来了全新的视野。
The many stunning discoveries I’ve introduced through this book were deeply perplexing at the time they were made. If we have to learn the mathematics behind those discoveries, it can be truly daunting. But I hope that my introduction of some of the biggest breakthroughs has brought to life just how exciting and beautiful they are. Just as Cézanne, Monet, van Gogh, Picasso, Matisse, Mondrian, Malevich, Kandinsky, Brancusi, Duchamp, Pollock, and Warhol forged new trails that challenged the art world, Newton and all those who have followed him gave us new vision.
二十世纪初物理学的先驱们——其中包括安托万·亨利·贝克勒尔、玛丽·居里、尼尔斯·玻尔、马克斯·普朗克、阿尔伯特·爱因斯坦、路易·德布罗意、埃尔温·薛定谔、沃尔夫冈·泡利、维尔纳·海森堡、保罗·狄拉克、恩里科·费米——他们提出的观点彻底颠覆了科学家们几个世纪甚至几千年来对现实的认知。在量子力学出现之前，我们认为粒子就是粒子，遵循牛顿定律；波就是波，遵循不同的物理定律。而现在我们知道，所有粒子都可以表现得像波，所有波也可以表现得像粒子。因此，十八世纪关于光是粒子还是波的问题（托马斯·杨在1801年似乎已经证明了光是波——参见第五章）如今已不再是问题，因为光既是粒子又是波。
The pioneers in physics of the early twentieth century—among them Antoine Henri Becquerel, Marie Curie, Niels Bohr, Max Planck, Albert Einstein, Louis de Broglie, Erwin Schrödinger, Wolfgang Pauli, Werner Heisenberg, Paul Dirac, Enrico Fermi—proposed ideas that completely undermined the way scientists had thought about reality for centuries, if not millennia. Before quantum mechanics we believed that a particle is a particle, obeying Newton’s laws, and that a wave is a wave obeying different physics. We now know that all particles can behave like waves and all waves can behave like particles. Thus the eighteenth-century issue, whether light is a particle or a wave (which seemed to be settled in 1801 by Thomas Young in favor of a wave—see chapter 5), is nowadays a non-issue as it is both.
在量子力学出现之前，人们普遍认为物理学是决定论的，也就是说，如果你重复做同一个实验一百次，你会得到完全相同的结果。但我们现在知道并非如此。量子力学研究的是概率，而非确定性。这在当时是如此令人震惊，以至于连爱因斯坦都无法接受。“上帝不会掷骰子”是他那句名言。然而，爱因斯坦错了！
Before quantum mechanics it was believed that physics was deterministic in the sense that if you do the same experiment a hundred times, you will get the exact same outcome a hundred times. We now know that that is not true. Quantum mechanics deals with probabilities—not certainties. This was so shocking that even Einstein never accepted it. “God does not throw dice” were his famous words. Well, Einstein was wrong!
在量子力学出现之前，我们认为粒子的位置和动量（质量与速度的乘积）原则上可以同时被精确测定。这是牛顿定律告诉我们的。但现在我们知道事实并非如此。虽然这可能与直觉相悖，但位置测定得越精确，动量的测定就越不精确；这就是著名的海森堡不确定性原理。
Before quantum mechanics we believed that the position of a particle and its momentum (which is the product of its mass and its velocity) could, in principle, simultaneously be determined to any degree of accuracy. That’s what Newton’s laws taught us. We now know that that is not the case. Nonintuitive as this may be, the more accurately you can determine its position, the less accurately can you determine its momentum; this is known as Heisenberg’s uncertainty principle.
爱因斯坦在他的狭义相对论中论证了空间和时间构成了一个四维现实，即时空。他假设光速是恒定的（每秒30万公里）。即使有人乘坐一列以光速50%（每秒15万公里）行驶的超高速列车向你驶来，并用车灯照射你的脸，你和他计算出的光速仍然是相同的。这非常违反直觉，因为你可能会认为，既然列车正向你驶来，那么作为观察者，你应该将30万和15万相加，得到每秒45万公里。但事实并非如此——根据爱因斯坦的说法，30万加15万仍然是30万！他的广义相对论或许……更令人叹为观止的是，爱因斯坦对维系宇宙的力提出了彻底的重新诠释，他认为引力是通过扭曲时空结构本身发挥作用的，通过几何原理将物体推入轨道，甚至迫使光线在同样的扭曲时空中弯曲。爱因斯坦表明牛顿物理学需要进行重大修正，并开启了现代宇宙学的先河：大爆炸、宇宙膨胀和黑洞。
Einstein argued in his theory of special relativity that space and time constituted one four-dimensional reality, spacetime. He postulated that the speed of light was constant (300,000 kilometers per second). Even if a person were approaching you on a superfast train going at 50 percent of the speed of light (150,000 kilometers per second), shining a headlight in your face, you and he would come up with the same figure for the speed of light. This is very nonintuitive, as you would think that since the train is approaching you, you who are observing the light aimed at you would have to add 300,000 and 150,000, which would lead to 450,000 kilometers per second. But that is not the case—according to Einstein, 300,000 plus 150,000 is still 300,000! His theory of general relativity was perhaps even more mind-boggling, offering a complete reinterpretation of the force holding the astronomical universe together, arguing that gravity functioned by distorting the fabric of spacetime itself, pushing bodies into orbit through geometry, even forcing light to bend through the same distorted spacetime. Einstein showed that Newtonian physics needed important revisions, and he opened the way to modern cosmology: the big bang, the expanding universe, and black holes.
上世纪70年代我在麻省理工学院开始教书时，我的性格使然，我更注重展现事物的美感和魅力，而不是那些学生们根本注意不到的细节。在我教授的每一门课程中，我都尽可能地将知识与学生们的现实世界联系起来，让他们看到一些他们从未想过但又触手可及的事物。每当学生提问时，我总是说：“这是一个很好的问题。” 你最不想做的就是让他们觉得自己很笨，而自己很聪明。
When I began lecturing at MIT in the 1970s, it was part of my personality to put more emphasis on the beauty and the excitement rather than the details that would be lost on the students anyway. In every subject I taught I always tried where possible to relate the material to the students’ own world—and make them see things they’d never thought of but were within reach of touching. Whenever students ask a question, I always say, “that’s an excellent question.” The absolute last thing you want to do is make them feel they’re stupid and you’re smart.
在我的电磁学课程中，有一个时刻对我来说弥足珍贵。这学期的大部分时间里，我们都在循序渐进地学习麦克斯韦方程组，这些方程组以令人惊叹的优雅方式描述了电和磁之间的关系——它们是同一现象（电磁学）的不同方面。这些方程组之间相互呼应的方式蕴含着一种难以置信的内在美。你无法将它们分开；它们共同构成了一个统一的场论。
There’s a moment in my course on electricity and magnetism that’s very precious to me. For most of the term we’ve been sneaking up, one by one, on Maxwell’s equations, the stunningly elegant descriptions of how electricity and magnetism are related—different aspects of the same phenomenon, electromagnetism. There’s an intrinsic beauty in the way these equations talk to one another that is unbelievable. You can’t separate them; together they’re one unified field theory.
于是，我把这四个优美的方程式投影到阶梯教室四面墙上的不同屏幕上。“看着它们，”我说，“用心感受它们。让它们渗入你的脑海。你一生中只有一次机会，能如此完整、如此优美、如此和谐地欣赏麦克斯韦方程组的全部四个方程式。这样的机会不会再有了。你的人生将从此改变。你失去了童贞。”为了纪念学生们生命中这意义非凡的一天，为了庆祝他们达到的智力巅峰，我带来了六百朵水仙花，每位学生一朵。
So I project these four beautiful equations on different screens on all the walls of the lecture hall. “Look at them,” I say. “Inhale them. Let them penetrate your brains. Only once in your life will you see all four of Maxwell’s equations for the first time in a way that you can appreciate them, complete and beautiful and talking to each other. This will never happen again. You will never be the same. You have lost your virginity.” In honor of this momentous day in the lives of the students, as a way of celebrating the intellectual summit they’ve reached, I bring in six hundred daffodils, one for each student.
多年以后，学生们给我写信，那时他们早已忘记了麦克斯韦方程组的细节，但他们仍然记得那天……水仙花，我用花朵为他们开启了全新的视觉世界。对我而言，这才是最高境界的教学。比起学生能否复述黑板上的内容，让他们记住所见之美远比让他们记住更重要。重要的不是你讲了什么，而是你发现了什么！
Students write me many years afterward, long after they’ve forgotten the details of Maxwell’s equations, that they remember the day of the daffodils, the day I marked their new way of seeing with flowers. To me this is teaching at the highest level. It’s so much more important to me for students to remember the beauty of what they have seen than whether they can reproduce what you’ve written on the blackboard. What counts is not what you cover, but what you uncover!
我的目标是让他们爱上物理，并让他们用不同的视角看待世界，这将终身受益！拓展他们的视野，让他们能够提出以前从未想过的问题。关键在于以一种能够与学生对世界的真正兴趣相联系的方式来开启物理世界。这就是为什么我总是试图带学生纵览整片森林，而不是带他们逐棵树逐棵树地爬上爬下。这也是我在这本书中努力为你做的。希望你享受这段旅程。
My goal is to make them love physics and to make them look at the world in a different way, and that is for life! You broaden their horizon, which allows them to ask questions they have never asked before. The point is to unlock the world of physics in such a way that it connects to the genuine interest students have in the world. That’s why I always try to show my students the forests, rather than take them up and down every single tree. That is also what I have tried to do in this book for you. I hope you have enjoyed the journey.
致谢
ACKNOWLEDGMENTS
如果没有我们杰出的文学经纪人温迪·斯特罗斯曼的智慧、远见、商业头脑和精神支持，《热爱物理》这本书恐怕只能停留在美好的愿望中。是她促成了我们两人的相识，为这本书找到了合适的出版商——自由出版社，她以多年出版经验磨练出的编辑眼光审阅了无数章节草稿，为这本书取了书名，并帮助我们始终专注于最终的成品。我们也很荣幸地拥有了她真挚的友谊，这份友谊在整个创作过程中给予了我们莫大的支持。
Without the intelligence, foresight, business sense, and moral support of our exceptional literary agent, Wendy Strothman, For the Love of Physics would have remained little more than wishful thinking. She brought the two of us together, found the right home for this book at Free Press, read numerous draft chapters with an editorial eye honed by her years as a publisher, gave the book its title, and helped keep us focused on the end product. We are also the happy and fortunate recipients of her staunch friendship, which buoyed us throughout the project.
自由出版社的编辑艾米丽·卢斯（Emily Loose）的贡献怎么强调都不为过。她对本书的构想极具感染力，她对散文叙事的精益求精也让我们受益匪浅。尽管出版业为了追求利润而承受着巨大的压力，艾米丽却坚持认真编辑本书，不断督促我们追求更清晰的表达、更流畅的过渡和更聚焦的主题。她的精湛技艺和一丝不苟的工作态度使本书更加出色。我们还要感谢艾米·瑞安（Amy Ryan）对稿件的细致润色和精湛的校对。
It would be hard to overstate the contributions of our editor, Emily Loose, at Free Press, whose vision for this book proved infectious and whose extraordinarily close attention to prose narrative provided an education for both of us. Despite the enormous pressure in the publishing industry to cut corners on behalf of the bottom line, Emily insisted on really editing this book, pushing us always to greater clarity, smoother transitions, and tighter focus. Her skill and intensity have made this a far better book. We are grateful as well to Amy Ryan for her deft copyediting of the manuscript.
沃尔特·莱文：
Walter Lewin:
每天我都会收到来自世界各地数十位观众的精彩邮件，他们通过网络观看我的讲座，邮件内容往往令人感动。这些讲座的举办要归功于理查德（迪克）·拉尔森的远见卓识。1998年，迪克担任麻省理工学院高级教育服务中心主任兼电子工程系教授时，他提议将我那些略显另类的讲座录制成视频，供麻省理工学院以外的学生观看。他为此获得了马萨诸塞州洛德基金会和大西洋慈善基金会的巨额资助。迪克的这项举措堪称电子学习的先驱！2001年，麻省理工学院开放课件平台正式上线，我的讲座也随之传遍世界各地，如今每年有超过一百万人观看。
Every day I receive wonderful, often very moving email from dozens of people all over the world who watch my lectures on the web. These lectures were made possible due to the vision of Richard (Dick) Larson. In 1998 when he was the director of the Center for Advanced Educational Services and a professor in the Department of Electrical Engineering at MIT, he proposed that my rather unconventional lectures be videotaped and made accessible to students outside MIT. He received substantial funding for this from the Lord Foundation of Massachusetts and from Atlantic Philanthropies. Dick’s initiative was the precursor of e-learning! When MIT’s OpenCourseWare opened its doors in 2001, my lectures reached all corners of the world and are now viewed by more than a million people each year.
过去两年里，甚至在我住院的七十天（差点丧命）期间，这本书也一直萦绕在我的心头。在家时，我和妻子苏珊·考夫曼不停地谈论它，以至于许多个夜晚都难以入眠。苏珊耐心地忍受着这一切，并设法让我保持乐观。她还以敏锐的编辑眼光审阅了其中的几个章节，并对其进行了显著的润色。
During the past two years, even during the seventy days that I was in the hospital (and almost died), this book was always on my mind. At home I talked about it incessantly with my wife, Susan Kaufman. It kept me awake many nights. Susan patiently endured all this and managed to keep my spirits up. She also trained her astute editorial eye on a number of chapters and improved them markedly.
我非常感谢我的表妹艾米·阿尔贝尔-卡卢斯和我的妹妹比娅·布洛克斯玛-莱温，她们与我分享了二战期间一些非常痛苦的回忆。我意识到这对她们来说是多么艰难，就像对我一样。我感谢我的挚友南希·斯蒂伯，我们相识三十年，她不仅一直纠正我的英语，还给了我许多宝贵的意见和建议。我还要感谢我的朋友和同事乔治·克拉克，没有他，我不可能成为麻省理工学院的教授。乔治让我阅读了美国科学与工程组织提交给空军剑桥研究实验室的原始提案，正是这份提案催生了X射线天文学。
I am very grateful to my cousin Emmie Arbel-Kallus and my sister, Bea Bloksma-Lewin, for sharing with me some of their very painful recollections of events during World War II. I realize how difficult this must have been for both of them, as it was for me. I thank Nancy Stieber, my close friend for thirty years, both for always correcting my English and for her invaluable comments and suggestions. I also want to thank my friend and colleague George Clark, without whom I would never have become a professor at MIT. George let me read the original American Science and Engineering proposal submitted to the Air Force Cambridge Research Laboratories that led to the birth of X-ray astronomy.
我感谢 Scott Hughes、Enectali Figueroa-Feliciano、Nathan Smith、Alex Filippenko、Owen Gingerich、Andrew Hamilton、Mark Whittle、Bob Jaffe、Ed van den Heuvel、Paul Murdin、George Woodrow、Jeff McClintock、John Belcher、Max Tegmark、Richard Lieu、Fred Rasio、已故的 John Huchra、Jeff Hoffman、Watti Taylor、Vicky Kaspi、Fred Baganoff、Ron Remillard、Dan Kleppner、Bob Kirshner、Paul Gorenstein、Amir Rizk、Chris Davlantes、Christine Sherratt、Markos Hankin、Bil Sanford 和 Andrew Neely 在我需要帮助时为我提供了帮助。
I am grateful to Scott Hughes, Enectali Figueroa-Feliciano, Nathan Smith, Alex Filippenko, Owen Gingerich, Andrew Hamilton, Mark Whittle, Bob Jaffe, Ed van den Heuvel, Paul Murdin, George Woodrow, Jeff McClintock, John Belcher, Max Tegmark, Richard Lieu, Fred Rasio, the late John Huchra, Jeff Hoffman, Watti Taylor, Vicky Kaspi, Fred Baganoff, Ron Remillard, Dan Kleppner, Bob Kirshner, Paul Gorenstein, Amir Rizk, Chris Davlantes, Christine Sherratt, Markos Hankin, Bil Sanford, and Andrew Neely for helping me, when help was needed.
最后，我非常感谢 Warren Goldstein 对我的耐心和灵活变通；有时，他一定感到压力很大（或许也很沮丧），因为要在太短的时间内完成太多的物理任务。
Finally I can’t thank Warren Goldstein enough for his patience with me and for his flexibility; at times he must have felt overwhelmed (and perhaps frustrated) with too much physics in too little time.
沃伦·戈德斯坦：
Warren Goldstein:
我要感谢以下人士愿意与我探讨沃尔特·莱温：劳拉·布洛克斯玛、比娅·布洛克斯玛-莱温、宝琳·布罗伯格-莱温、苏珊·考夫曼、艾伦·克雷默、维斯·德·希尔、伊曼纽尔（查克）·莱温、大卫·普利、南希·斯蒂伯和彼得·斯特鲁伊肯。即使他们的观点未在《热爱物理》一书中被引用，但他们每一位都极大地加深了我对沃尔特·莱温的理解。爱德华·格雷、雅各布·哈尼、劳伦斯·马歇尔、詹姆斯·麦克唐纳和鲍勃·塞尔默尽其所能地帮助沃尔特和我避免在他们各自的专业领域犯错；尽管我们更愿意将责任推卸给他们，但我们对任何遗留的错误负全部责任。我还要感谢2011年毕业于哈特福德大学的威廉·J·利奥，感谢他在关键时刻给予的帮助。我认识的三位最聪明的作家——马克·冈瑟、乔治·坎纳和伦纳德·戴维斯——在项目初期都给了我宝贵的建议。哈特福德大学的约瑟夫·沃克院长和弗雷德·斯威策助理教务长以不同的方式帮助我抽出时间完成了这本书。我由衷地感谢我的妻子唐娜·沙佩尔——一位杰出的牧师和组织者，也是三十本书的作者（据我统计）——她理解并支持我沉浸于一个陌生的世界。我们的孙子卡莱布·本杰明·卢里亚于2010年10月18日出生；看着他用日常生活中的物理原理进行一系列非凡的实验，真是令人欣喜。最后，我要在此向沃尔特·莱温表达我深深的感激之情，在过去的几年里，他教给我的物理知识比我们俩想象的还要多，并重新点燃了我心中沉睡已久的热情。
I would like to thank the following people for their willingness to talk with me about Walter Lewin: Laura Bloksma, Bea Bloksma-Lewin, Pauline Broberg-Lewin, Susan Kaufman, Ellen Kramer, Wies de Heer, Emanuel (Chuck) Lewin, David Pooley, Nancy Stieber, Peter Struycken. Even if they are not quoted in For the Love of Physics, each one added substantially to my understanding of Walter Lewin. Edward Gray, Jacob Harney, Laurence Marschall, James McDonald, and Bob Celmer did their best to keep Walter and me from making mistakes in their fields of expertise; as much as we’d prefer to put the onus on them, we take full responsibility for any remaining errors. I also want to thank William J. Leo, a 2011 graduate of the University of Hartford, for his assistance at a critical moment. Three of the smartest writers I know—Marc Gunther, George Kannar, and Lennard Davis—all gave me invaluable advice early in the project. In different ways Dean Joseph Voelker and Assistant Provost Fred Sweitzer of the University of Hartford made it possible for me to find the time to finish this book. I am deeply grateful to my wife, Donna Schaper—minister and organizer extraordinaire, and author of thirty books at last count—for understanding and celebrating my immersion in a foreign world. Our grandson, Caleb Benjamin Luria, came into the world October 18, 2010; it has been a delight to watch him undertake his own series of remarkable experiments in the physics of everyday life. Finally, I want here to express my deep gratitude to Walter Lewin, who taught me more physics in the last few years than either of us would have thought possible and rekindled a passion in me that had lain dormant far too long.
附录1
APPENDIX 1
哺乳动物股骨
Mammal Femurs
假设哺乳动物的质量与其体积成正比是合理的。我们不妨拿一只幼犬和一只体型是它四倍的成年犬做个比较。我假设这只成年犬的所有线性尺寸——身高、体长、腿长和腿粗、头部宽度等等——都是幼犬的四倍。如果真是这样，那么这只成年犬的体积（以及质量）大约是幼犬的六十四倍。
It’s reasonable to assume that the mass of a mammal is proportional to its volume. Let’s take a puppy and compare it with a full-grown dog that is four times bigger. I am assuming that all linear dimensions of the bigger dog are four times larger than that of the puppy—its height, its length, the length and the thickness of its legs, the width of its head, everything. If that is the case, then the volume (and thus the mass) of the bigger dog is about sixty-four times that of the puppy.
理解这一点的一个方法是取一个边长分别为a、b和c 的立方体。这个立方体的体积是a × b × c。当所有边长都增大四倍时，体积变为 4a × 4b × 4c ，即 64abc 。如果我们用更数学化的方式来表达，我们可以说哺乳动物的体积（也就是质量）与其长度的三次方成正比。如果大狗比小狗大四倍，那么它的体积大约是小狗的 4³ 倍，也就是 64。所以，如果我们把股骨的长度记为“ l ”，那么通过比较不同体型的哺乳动物，它们的质量应该大致与l³成正比。
One way to see this is by taking a cube with sides a, b, and c. The volume of this cube is a × b × c. When you make all sides four times larger, the volume becomes 4a × 4b × 4c, which is 64abc. If we express this a bit more mathematically, we can say that the volume (thus the mass) of the mammal is proportional to its length to the third power. If the bigger dog is four times larger than the puppy, then its volume should be about 4 cubed (43) times larger, which is 64. So, if we call the length of the femur “l,” then by comparing mammals of different size, their mass should be roughly proportional to l cubed (l3).
好的，这就是质量。现在，哺乳动物股骨支撑所有重量的强度必须与其厚度成正比，对吧？更粗的骨头可以支撑更大的重量——这很直观。如果我们把这个想法转化成……从数学角度来看，股骨的强度应该与其横截面积成正比。该横截面近似于一个圆，我们知道圆的面积公式为πr² ，其中r是圆的半径。因此，如果d是圆的直径，则面积与d²成正比。
Okay, that’s mass. Now, the strength of the mammal’s femur supporting all that weight has to be proportional to its thickness, right? Thicker bones can support more weight—that’s intuitive. If we translate that idea to mathematics, the strength of the femur should be proportional to the area of the cross section of the bone. That cross section is roughly a circle, and we know that the area of a circle is πr2, where r is the radius of the circle. Thus, the area is proportional to d2 if d is the diameter of the circle.
我们把股骨的厚度记为“ d ”（代表直径）。那么，根据伽利略的理论，哺乳动物的质量将与d²成正比。
Let’s call the thickness of the femur “d” (for diameter). Then, following Galileo’s idea, the mass of the mammal would be proportional to d2
（这样骨骼才能承受哺乳动物的重量），但它也与l³成正比（无论伽利略的观点如何，情况总是如此）。因此，如果伽利略的观点是正确的，那么d²应该与l³成正比，这等同于说d与l³ / ²成正比。
(so that the bones can carry the weight of the mammal), but it is also proportional to l3 (that is always the case, independent of Galileo’s idea). Thus, if Galileo’s idea is correct, d2 should be proportional to l3, which is the same as stating that d is proportional to l3/2.
如果我比较两种哺乳动物，其中一种比另一种大五倍（因此，它的股骨长度l大约是较小哺乳动物的五倍），那么我可以预期，它的股骨厚度d大约是较小动物股骨厚度的 5 又3/2 = 11 倍。在课堂上，我展示了大象股骨的长度l大约是老鼠股骨长度的 100 倍；因此，如果伽利略的观点是正确的，我们可以预期，大象股骨的厚度d大约是老鼠股骨厚度的 100又3/2 = 1000 倍。
If I compare two mammals and one is five times bigger than the other (thus the length l of its femur is about five times larger than that of the smaller mammal), I may expect that the thickness, d, of its femur is about 53/2 = 11 times greater than the thickness of the smaller animal’s femur. In lectures I showed that the length l of the femur of an elephant was about 100 times larger than the length of the femur of a mouse; we may therefore expect, if Galileo’s idea is correct, that the thickness, d, of the elephant’s femur is about 1003/2 = 1,000 times thicker than that of the mouse.
因此，对于非常重的哺乳动物来说，骨骼的厚度在某种程度上必须与其长度相同，甚至更大，这将导致一些非常不实用的哺乳动物，而这正是哺乳动物体型存在最大限制的原因。
Thus at some point, for very heavy mammals, the thickness of the bones would have to be the same as their lengths—or even greater—which would make for some pretty impractical mammals, and that would then be the reason why there is a maximum limit on the size of mammals.
附录2
APPENDIX 2
牛顿定律的应用
Newton’s Laws at Work
牛顿万有引力定律可以写成：
Newton’s law of universal gravitation can be written as
这里，F <sub>grav</sub>是质量为m <sub> 1 </sub>的物体和质量为m <sub> 2 </sub>的物体之间的引力，r是它们之间的距离。G称为引力常数。
Here, Fgrav is the force of gravitational attraction between an object of mass m1 and one of mass m2, and r is the distance between them. G is called the gravitational constant.
牛顿定律使得人们至少在理论上可以计算出太阳和一些行星的质量。
Newton’s laws made it possible to calculate, at least in principle, the mass of the Sun and some planets.
我们来看看它是如何运作的。我先从太阳开始。假设m1是太阳的质量，m2是一颗行星（任何行星）的质量。我假设行星的轨道是一个半径为r的圆，并设行星的公转周期为T （地球的T为 365.25 天，水星为 88 天，木星接近 12 年）。
Let’s see how this works. I’ll start with the Sun. Suppose m1 is the mass of the Sun, and that m2 is the mass of a planet (any planet). I will assume that the planetary orbit is a circle of radius r and let the orbital period of the planet be T (T is 365.25 days for the Earth, 88 days for Mercury, and almost twelve years for Jupiter).
如果轨道是圆形或近似圆形（十七世纪已知的六颗行星中有五颗的轨道是圆形的），那么行星的轨道速度是恒定的，但速度方向却在不断变化。然而，任何物体的速度方向一旦发生变化，即使速度本身没有变化，也必然存在加速度，因此，根据牛顿第二定律，必然存在力来提供这种加速度。
If the orbit is circular or nearly so (which is the case for five of the six planets known in the seventeenth century), the speed of a planet in orbit is constant, but the direction of its velocity is always changing. However, whenever the direction of the velocity of any object changes, even if there is no change in speed, there must be an acceleration, and thus, according to Newton’s second law, there must be a force to provide that acceleration.
它被称为向心力（F <sub>c</sub>），方向始终与运动的行星指向太阳的方向一致。当然，由于牛顿是牛顿，他非常清楚如何计算这个力（我在讲课中会推导这个公式）。这个力的大小是
It’s called the centripetal force (Fc), and it is always exactly in the direction from the moving planet toward the Sun. Of course, since Newton was Newton, he knew exactly how to calculate this force (I derive the equation in my lectures). The magnitude of this force is
这里v是行星绕太阳公转的速度。但这个速度等于轨道周长 2πr²除以行星绕太阳公转一周所需的时间T。因此，我们也可以写成：
Here v is the speed of the planet in orbit. But this speed is the circumference of the orbit, 2πr, divided by the time, T, it takes to make one revolution around the Sun. Thus we can also write:
这种力从何而来？它究竟源自何处？牛顿意识到，这必定是太阳的引力。因此，上述方程式中的两个力实际上是同一种力，它们彼此相等。
Where does this force come from? What on earth (no pun implied) is the origin of this force? Newton realized that it must be the gravitational attraction by the Sun. Thus the two forces in the above equations are one and the same force; they are equal to each other:
如果我们通过重新排列变量来进一步推导这个公式（这是你复习一下高中代数的好机会），我们会发现太阳的质量是
If we massage this a bit further by rearranging the variables (this is your chance to brush up on your high school algebra), we find that the mass of the Sun is
注意，行星的质量 ( m₂ )已不再出现在公式 5 中；它不再起作用；我们只需要行星到太阳的平均距离和它的公转周期 ( T )。这难道不让你感到惊讶吗？毕竟，m₂出现在公式 1 和公式 2 中。但正是因为它同时出现在这两个公式中，才使得通过将F <sub>grav</sub>等于F<sub> c</sub>来消除m₂ 。这就是这种方法的精妙之处，而这一切都要归功于艾萨克爵士！
Notice that the mass of the planet (m2) is no longer present in equation 5; it does not enter into the picture; all we need is the planet’s mean distance to the Sun and its orbital period (T). Doesn’t that surprise you? After all, m2 shows up in equation 1 and also in equation 2. But the fact that it is present in both equations is the very reason that m2 is eliminated by setting Fgrav equal to Fc. That’s the beauty of this method, and we owe all this to Sir Isaac!
公式 5 表明，
所有行星的情况都相同。尽管它们到太阳的距离和轨道都大相径庭。对于所有天体而言，轨道周期都是相同的。早在牛顿之前，德国天文学家兼数学家约翰内斯·开普勒就于1619年发现了这一惊人的结果。然而，轨道半径的立方与轨道周期的平方之比为何是恒定的，却始终无人知晓。直到68年后，天才牛顿才证明，这正是他的宇宙定律的自然推论。
Equation 5 indicates that is the same for all planets. Even though they all have very different distances to the Sun and very different orbital periods, is the same for all. The German astronomer and mathematician Johannes Kepler had already discovered this amazing result in 1619, long before Newton. But why this ratio—between the cube of the radius and square of the orbital period—was constant was not understood at all. It was the genius Newton who showed sixty-eight years later that it is the natural consequence of his laws.
总之，公式 5 告诉我们，如果我们知道任何行星到太阳的距离 ( r )、行星的轨道周期 ( T ) 和G，我们就可以计算太阳的质量 ( m1 )。
In summary, equation 5 tells us that if we know the distance from any planet to the Sun (r), the orbital period of the planet (T), and G, we can calculate the mass of the Sun (m1).
早在十七世纪之前，人们就已经能够非常精确地计算出行星的轨道周期。太阳与行星之间的距离也同样在十七世纪之前就被人们非常精确地计算出来，但当时的计算仅限于相对距离。换句话说，天文学家知道金星到太阳的平均距离是地球的72.4%，木星到太阳的平均距离是地球的5200倍。然而，这些距离的绝对值却完全是另一回事。在十六世纪，也就是伟大的丹麦天文学家第谷·布拉赫的时代，天文学家们认为地球到太阳的距离比实际距离（接近1.5亿公里，约9300万英里）小20倍。十七世纪初，开普勒计算出了更精确的太阳距离，但仍然比实际距离小7倍。
Orbital periods were known to a high degree of accuracy long before the seventeenth century. The distances between the Sun and the planets were also known to a high degree of accuracy long before the seventeenth century but only on a relative scale. In other words, astronomers knew that Venus’s mean distance to the Sun was 72.4 percent of Earth’s and that Jupiter’s mean distance was 5.200 times larger than Earth’s. However, the absolute values of these distances were an entirely different story. In the sixteenth century, in the day of the great Danish astronomer Tycho Brahe, astronomers believed that the distance from the Earth to the Sun was twenty times smaller than what it actually is (close to 150 million kilometers, about 93 million miles). In the early seventeenth century Kepler came up with a more accurate distance to the Sun, but still seven times smaller than what it is.
由于公式 5 表明太阳的质量与（到行星的）距离的立方成正比，如果距离r比实际距离小 7 倍，那么太阳的质量也会比实际距离小 7³ 倍，即 343——这完全没有用处。
Since equation 5 indicates that the mass of the Sun is proportional to the distance (to a planet) cubed, if the distance r is too low by a factor of seven, then the mass of the Sun will be too low by a factor of 73, which is 343—not very useful at all.
1672年，意大利科学家乔瓦尼·卡西尼测量了地球到太阳的距离，精度达到了约7%（在当时令人印象深刻），这意味着r³的误差仅为22%左右。而G的误差可能至少为30%。因此，我猜测到17世纪末，太阳质量的测量精度可能不超过50%。
A breakthrough came in 1672 when the Italian scientist Giovanni Cassini measured the distance from the Earth to the Sun to an accuracy of about 7 percent (impressive for those days), which meant that the uncertainty in r3 was only about 22 percent. The uncertainty in G was probably at least 30 percent. So my guess is that by the end of the seventeenth century the mass of the Sun may have been known to an accuracy no better than 50 percent.
由于太阳到行星的相对距离已知得相当精确，因此，到十七世纪末，太阳到地球的绝对距离已知得达到 7% 的精度，这意味着其他五个已知行星到太阳的绝对距离也可以计算到同样的 7% 的精度。
Since the relative distances from the Sun to the planets were known to a high degree of accuracy, knowing the absolute distance from the Sun to the Earth to 7 percent accuracy meant that the absolute distances to the Sun of the other five known planets could also be calculated to that same 7 percent accuracy by the end of the seventeenth century.
上述计算太阳质量的方法也可用于测量木星、土星和地球的质量。这三颗行星都曾拥有已知的卫星；1610年，伽利略·伽利莱发现了木星的四颗卫星，即现在所说的伽利略卫星。如果m₁是木星的质量，m₂是其一颗卫星的质量，那么我们可以用公式5计算木星的质量，方法与计算太阳质量的方法相同，只是这里的r是木星与其卫星之间的距离，T是该卫星绕木星的公转周期。这四颗伽利略卫星（木星共有63颗卫星！）的公转周期分别为1.77天、3.55天、7.15天和16.69天。
The above method to calculate the mass of the Sun can also be used to measure the mass of Jupiter, Saturn, and the Earth. All three planets had known moons in orbit; in 1610 Galileo Galilei discovered four moons of Jupiter, now known as the Galilean moons. If m1 is the mass of Jupiter, and m2 the mass of one of its moons, then we can calculate the mass of Jupiter, using equation 5, in the same way that we can calculate the mass of the Sun, except that now r is the distance between Jupiter and its moon, and T is the orbital period of that moon around Jupiter. The four Galilean moons (Jupiter has sixty-three moons!) have orbital periods of 1.77 days, 3.55 days, 7.15 days, and 16.69 days.
随着时间的推移，距离和重力加速度G的测量精度都得到了极大的提高。19世纪时，重力加速度G的测量精度约为1%。如今，其精度已达到约0.01%。
Accuracies in distances and in G have greatly improved over time. By the nineteenth century G was known to about 1 percent accuracy. It is now known to an accuracy of about 0.01 percent.
让我举个数值例子。利用公式 5，我们来计算地球的质量 ( m₁ )，其中月球的质量为 m₂。为了正确使用公式 5，距离 r 的单位应该是米，时间 T 的单位应该是秒。如果我们用 6.673 × 10⁻¹¹作为重力加速度G ，就能得到以千克为单位的质量。
Let me show you a numerical example. Using equation 5, let’s calculate together the mass of the Earth (m1) by using the orbit of our Moon (with mass m2). To use equation 5 properly, the distance, r, should be in meters, and T should be in seconds. If we then use 6.673 × 10–11 for G, we get the mass in kilograms.
地球到月球的平均距离 ( r ) 为 3.8440 × 10⁸米（约 239,000 英里）；其公转周期 ( T ) 为 2.3606 × 10⁶秒（27.32 天）。如果我们把这些数值代入公式 5，就会发现地球的质量为 6.030 × 10²⁴千克。目前地球质量的最佳值接近 5.974 × 10²⁴千克，仅比我计算出的值低 1%！为什么会有这样的差异呢？原因之一是我们使用的公式假设月球的轨道是圆形的，而实际上月球的轨道是椭圆形的。因此，地球到月球的最近距离约为 224,000 英里；最远距离约为 252,000 英里。当然，牛顿定律也能轻松处理椭圆轨道，但其中的数学推导可能会让你大吃一惊。或许你已经被震撼到了！
The mean distance to the Moon (r) is 3.8440 × 108 meters (about 239,000 miles); its orbital period (T) is 2.3606 × 106 seconds (27.32 days). If we plug these numbers into equation 5, we find that the mass of the Earth is 6.030 × 1024 kilograms. The best current value of Earth’s mass is close to 5.974 × 1024 kilograms, which is only 1 percent lower than what I calculated! Why the difference? One reason is that the equation we used assumed that the Moon’s orbit is circular, when in fact it is elongated, what we call elliptical. As a result, the smallest distance to the Moon is about 224,000 miles; the largest is about 252,000 miles. Of course, Newton’s laws can also easily deal with elliptical orbits, but the math may blow your mind. Perhaps it already has!
地球质量计算结果略有偏差还有另一个原因。我们假设月球绕地球公转，且该圆的圆心即为地球中心。因此，在公式 1 和公式 3 中，我们假设r为地球与月球之间的距离。这在公式 1 中是正确的；然而，正如我在第 13 章中更详细讨论的那样，月球和地球实际上各自绕着地月系统的质心公转，而该质心位于地球表面以下约一千英里处。因此，公式 3 中的r 值略小于公式 1 中的r 值。
There is another reason why our result for the mass of the Earth is a little off. We assumed that the Moon circles around the Earth and that the center of that circle is the center of the Earth. Thus in equations 1 and 3, we assumed that r is the distance between the Earth and the Moon. That is correct in equation 1; however, as I discuss in more detail in chapter 13, the Moon and the Earth actually each orbit the center of mass of the Moon-Earth system, and that is about a thousand miles below the Earth’s surface. Thus r, in equation 3, is a little less than r in equation 1.
既然我们生活在地球上，那么还有其他方法可以计算我们星球的质量。一种方法是测量地表附近的重力加速度。任何质量为m（m可以是任意值）的物体在自由落体时，都会受到一个接近 9.82 米/秒² 的加速度g 的作用。地球的平均半径接近 6.371 × 10⁶米（约 3,960 英里）。
Since we live on Earth, there are other ways of calculating the mass of our home planet. One is by measuring the gravitational acceleration near the surface. When dropped, any object of mass m (m can have any value) will be accelerated with an acceleration, g, close to 9.82 meters per second per second.* Earth’s average radius is close to 6.371 × 106 meters (about 3,960 miles).
现在让我们重新审视牛顿方程1。由于F = ma（牛顿第二定律），那么
Now let’s revisit Newton’s equation 1. Since F = ma (Newton’s second law), then
这里，r是地球半径。已知G = 6.673 × 10⁻¹¹，g = 9.82 米每秒，r = 6.371 × 10⁶米，我们可以计算出地球的质量m（单位：千克）（不妨试试！）。如果我们对公式 6 进行一些简化，就能得到
Here, r is the radius of the Earth. With G = 6.673 × 10–11, g = 9.82 meters per second per second, and r = 6.371 × 106 meters, we can calculate mearth in kilograms (you try it!). If we simplify equation 6 somewhat, we get
我发现地球的质量m为 5.973 × 10 24千克（令人印象深刻，对吧？）。
I find that mearth is 5.973 × 1024 kilograms (impressive, right?).
注意，我们扔下的物体的质量m并没有显示出来。在公式 7 中！这不应该让你感到惊讶，因为地球的质量不可能取决于你扔下的物体的质量。
Notice that the mass, m, of the object we dropped does not show up in equation 7! That should not surprise you, as the mass of the Earth could not possibly depend on the mass of the object that you drop.
你或许也想知道，牛顿曾认为地球的平均密度在每立方米5000到6000千克之间。这并非基于任何天文信息，也完全与他的任何定律无关。这只是他基于现有知识做出的最佳“推测”。事实上，地球的平均密度是每立方米5540千克。如果允许我将牛顿的推测写成每立方米5500±500千克，那么他的不确定度只有10%（令人惊叹！）。
You might also be interested in knowing that Newton believed that the average density of the Earth was between 5,000 and 6,000 kilograms per cubic meter. This was not based on any astronomical information; it was completely independent of any of his laws. It was his best “educated” guess. The average density of the Earth is, in fact, 5,540 kilograms per cubic meter. If you allow me to write Newton’s guess as 5,500 ± 500 kilograms per cubic meter, his uncertainty was only 10 percent (amazing!).
我不知道牛顿的猜测在他那个时代是否被认真对待过，但假设它被认真对待过。由于地球半径在十七世纪已经为人所知，其质量的计算精度可以达到10%（质量等于体积乘以密度）。那么，就可以利用公式7计算出引力常数G，精度同样可以达到10%。我之所以提到这一点，是因为它让我感到好奇：如果接受牛顿对地球平均密度的猜测，那么在十七世纪末，引力常数G的计算精度可能已经达到了10%！
I do not know if Newton’s guess was ever taken seriously in his day, but suppose it was. Since Earth’s radius was well known in the seventeenth century, its mass could have been calculated to an accuracy of 10 percent (mass is volume times density). Equation 7 could then be used to calculate G also to an accuracy of 10 percent. I am telling you this because it intrigues me that, accepting Newton’s guess for the mean density of the Earth, at the end of the seventeenth century the gravitational constant, G, could already have been known to an accuracy of 10 percent!
指数
INDEX
吸收线，237 –39
absorption lines, 237–39
学术地球，x
Academic Earth, x
巴伐利亚科学院，155
Academy of Sciences, Bavaria, 155
圣彼得堡科学院，146
Academy of Sciences, St. Petersburg, 146
苏联科学院，253
Academy of Sciences, Soviet, 253
三磷酸腺苷（ATP），169
adenosine triphosphate (ATP), 169
“空气动力升力、伯努利效应、反作用升力”（约翰逊），74
“Aerodynamic Lift, Bernoulli Effect, Reaction Lift” (Johnson), 74
空气，重量，60-61
air, weight of, 60–61
磁悬浮列车和，164
maglev trains and, 164
摆锤和，52
pendulums and, 52
空军剑桥研究实验室（AFCRE），193-94
Air Force Cambridge Research Laboratories (AFCRE), 193–94
在地球表面，63-64
on Earth’s surface, 63–64
测量结果为61 – 63
measuring, 61–63
风和，64
wind and, 64
阿尔比，爱德华，123
Albee, Edward, 123
α衰变，183
alpha decay, 183
alternating current (AC), 158, 161
铝，151
aluminum, 151
亚马逊之星（贝拉特里克斯），237
Amazon Star (Bellatrix), 237
琥珀色，126
amber, 126
美国物理学会，213
American Physical Society, 213
American Science and Engineering (ASE), 17, 193–94
Ampère, André-Marie, 138, 154, 166
安培定律，166
Ampère’s law, 166
振幅，118
amplitude, 118
能量和，105
energy and, 105
声波，104-6
of sound waves, 104–6
音叉，106
of tuning fork, 106
AM广播频段，191-92
AM radio band, 191–92
造父变星和，33
Cepheids and, 33
角动量，224
angular momentum, 224
反物质，187
antimatter, 187
大坛座（星座），195
Ara (constellation), 195
弧秒，29-30
arc second, 29–30
艺术，262-68
art, 262–68
author’s collaborations in, 263, 264–67
作者收藏，262
author’s collection of, 262
先驱者，267-68
pioneers of, 267–68
宇航员，24-25，44，58，65
人工重力，以及，56
artificial gravity and, 56
自由落体，47-48
free fall and, 47–48
荷兰天文卫星（ANS），248
Astronomical Netherlands Satellite (ANS), 248
天文学，2-3，50，189
错误框和，195
error box and, 195
重力势能和，172-73，174
gravitational potential energy and, 172–73, 174
测量结果和，27-28
measurements and, 27–28
望远镜和，190
telescopes and, 190
32名女性
women in, 32n
另见天文学的具体类型
see also specific kinds of astronomy
天体物理学杂志快报，215
Astrophysical Journal Letters, 215
大气光学，85
Atmospheric Optics, 85
atmospheric pressure, 63–64, 66–68
原子弹，184
atomic bomb, 184
输入电力，130
electricity in, 130
核，130
nucleus of, 130
正负电荷，130 –31
positive and negative charges in, 130–31
尺寸为130
size of, 130
X射线和，192
X-rays and, 192
ATP（三磷酸腺苷），169
ATP (adenosine triphosphate), 169
听力计，106
audiometer, 106
南极光（aurora australis），153 –54
aurora australis (southern lights), 153–54
极光（北极光），10，153-54，245
aurora borealis (northern lights), 10, 153–54, 245
澳大利亚，186，202-5，209
巴比伦人，115
Babylonians, 115
班卓琴，112
banjo, 112
低音提琴，113
bass fiddle, 113
巴松管，120
bassoon, 120
电池，138、158、161、181
制作，170
making, 170
巴伐利亚科学院，155
Bavarian Academy of Sciences, 155
贝克勒尔，安托万·亨利，268
Becquerel, Antoine Henri, 268
Belian，RD，248
Belian, R. D., 248
贝尔，乔斯林，32n，198，224-25
Bell, Jocelyn, 32n, 198, 224–25
Bellatrix（亚马逊之星），237
Bellatrix (Amazon Star), 237
伯努利，丹尼尔，73-74
Bernoulli, Daniel, 73–74
伯努利原理，73-74
Bernoulli’s principle, 73–74
贝塞尔，弗里德里希·威廉，236-37
Bessel, Friedrich Wilhelm, 236–37
参宿四（恒星），237
Betelgeuse (star), 237
贝维斯，约翰，196
Bevis, John, 196
圣经，80
Bible, 80
宇宙大爆炸理论，9，19，35-36，188，223，270
big bang, theory of, 9, 19, 35–36, 188, 223, 270
波长为108 –9
wavelength of, 108–9
鸟类、磁性和，152
birds, magnetism and, 152
铋，151
bismuth, 151
blackbody radiation, 192, 237, 246
在X射线爆发中，250-51
in X-ray bursts, 250–51
animations and recreations of, 225, 229
计算大小为228
calculating size of, 228
在核心坍缩超新星中，223
in core-collapse supernova, 223
创建于220 –21 年
creation of, 220–21
多普勒效应，232-33
Doppler effect and, 232–33
逃逸速度为227 –28
escape velocity of, 227–28
蒸发，230
evaporation of, 230
事件视界，参见事件视界
event horizon of, see event horizon
陷入，231-34
falling into, 231–34
广义相对论和，228
general relativity and, 228
重力井，226，227-28
霍金辐射，231
Hawking radiation of, 231
LHC及其创建，229-30
LHC and creation of, 229–30
被吞噬的物质，225-26
matter swallowed up by, 225–26
微型，229-31
micro, 229–31
在英仙座星系团中，108
in Perseus cluster, 108
singularity of, 228–29, 233–34
声波，108
sound waves of, 108
意大利面化，233-34
spaghettification in, 233–34
光速，以及232
speed of light and, 232
潮汐力和，233-34
tidal forces and, 233–34
在X射线双星中，241-42，244
in X-ray binaries, 241–42, 244
X射线爆发和，257
X-ray bursts and, 257
蓝色喷气式闪电，148
blue jet lightning, 148
另见多普勒效应
see also Doppler effect
体温，176-77，179
玻尔，尼尔斯，268
Bohr, Niels, 268
博伊曼斯·范布宁根博物馆，266
Boijmans van Beuningen Museum, 266
博尔顿，汤姆，241-42
Bolton, Tom, 241–42
瓶颈，121-22
bottlenecks, 121–22
博伊尔，罗伯特，126
Boyle, Robert, 126
第谷·布拉赫，126、189、190、281
Brahe, Tycho, 126, 189, 190, 281
布朗库西，康斯坦丁，268
Brancusi, Constantin, 268
铜管乐器，120 –21
brass instruments, 120–21
bremsstrahlung emissions, 192, 194
布鲁斯特，大卫，93岁
Brewster, David, 93
布鲁斯特角，93
Brewster angle, 93
亮度、光度和，32-33
brightness, luminosity and, 32–33
布罗肯幽灵（荣耀），97-98
Brocken spectres (glories), 97–98
布罗格利，路易·德，268
Broglie, Louis de, 268
布鲁克林大桥，124
Brooklyn Bridge, 124
布劳顿悬索桥，124
Broughton Suspension Bridge, 124
布鲁诺，乔尔达诺，189
Bruno, Giordano, 189
177 BTU
BTUs, 177
佛光，98
Buddha’s light, 98
Busza，Wit，158
Busza, Wit, 158
卡路里，174
calorie, 174
定义，177
defined, 177
电容器，155
capacitor, 155
二氧化碳，169
carbon dioxide, 169
卡西尼，乔瓦尼，281
Cassini, Giovanni, 281
大提琴，112
cello, 112
Centaurus (constellation), 196, 213, 243
高级视觉研究中心，263
Center for Advanced Visual Studies, 263
中央倡导者报，211
Centralian Advocate, 211
离心力，57
centrifugal force, 57
向心力，56-57，136，280
centripetal force, 56–57, 136, 280
Cen X-1（X射线源），196
Cen X-1 (X-ray source), 196
Cen X - 2 （ X射线源），213，215，255
Cen X-2 (X-ray source), 213, 215, 255
Cen X-3（X射线源），243
Cen X-3 (X-ray source), 243
光度-周期关系，32-34
luminosity-period relationship of, 32–34
II 型，33
Type II, 33
欧洲核子研究中心（CERN），229
CERN (European Organization for Nuclear Research), 229
塞尚，保罗，268
Cézanne, Paul, 268
查德威克，詹姆斯，217
Chadwick, James, 217
Chandrasekhar, S., 215
Chandrasekhar, S., 215
钱德拉塞卡极限，219
Chandrasekhar limit, 219
Chandra X-Ray Observatory, 198, 222
切尔诺贝利灾难，185
Chernobyl disaster, 185
中国，古代，150，151，183
China, People’s Republic of, 98, 185
克拉尼盘，118-19
Chladni plates, 118–19
氧化铬，151
chromium oxide, 151
楚，史蒂文，181
Chu, Steven, 181
单簧管，119
clarinet, 119
克拉克，阿尔文，237
Clark, Alvan, 237
克拉克，乔治，2，18，198，199，200，208，213，214
Clark, George, 2, 18, 198, 199, 200, 208, 213, 214
课堂和家庭演示：
classroom and home demonstrations:
空气柱，121-22
of air column, 121–22
气流，73-75
of air flow, 73–75
气压，59-60，64-65，71
of air pressure, 59–60, 64–65, 71
人工重力，55-58
of artificial gravity, 55–58
制造电机，158-61
of building a motor, 158–61
能量守恒，168-69，173-74
of conservation of energy, 168–69, 173–74
雾虹的形成，96-97
creating fogbows, 96–97
用吸管喝水，75-77
of drinking with a straw, 75–77
电势，140 –41
of electrical potential, 140–41
电磁学，156
of electromagnetism, 156
能量转换，170
of energy conversion, 170
菲斯塔韦尔，183-84
of Fiestaware, 183–84
玻璃弓，100-102
of glassbows, 100–102
高频声音，106
of high-frequency sound, 106
of homemade rainbow, 86–88, 87
静水压力，67-70
of hydrostatic pressure, 67–70
液态磁体，151
of liquid magnet, 151
磁悬浮，161-62，164
of magnetic levitation, 161–62, 164
制造电池，170
of making a battery, 170
测量，23-24
of measurement, 23–24
摆锤，52-55
of pendulums, 52–55
破碎的酒杯，118
of shattered wineglass, 118
音板，114
of sounding board, 114
火花，139-40
of sparks, 139–40
of static electricity, 127–28, 132–36
失重，47-48
of weightlessness, 47–48
钴，151
cobalt, 151
颜色（音色），112
color (timbre), 112
彗星，10
comets, 10
科明斯基，林恩，255
Cominsky, Lynn, 255
换向器，159
commutator, 159
共动距离，35
co-moving distance, 35
紧凑型荧光灯（CFL），186
compact fluorescent lights (CFL), 186
致密恒星X射线源（Lewin等人编），259
Compact Stellar X-Ray Sources (Lewin, et al., eds.), 259
完备场论，165
complete field theory, 165
导体，传导，128-29，131-32，136
conductors, conduction, 128–29, 131–32, 136
皮肤效应，145-46
skin effect and, 145–46
康纳，JP，248
Conner, J. P., 248
电荷守恒定律，128
conservation of electric charge, law of, 128
建设性干涉，95
constructive interference, 95
哥白尼，尼古拉，189
Copernicus, Nicolaus, 189
铜，151，156-57
法国科尔多瓦，259
Córdova, France, 259
core-collapse supernova, 217–20, 226
黑洞形成于223年
black hole formed in, 223
燃烧周期为，218 –19
burning cycles of, 218–19
Chandra 限制在219
Chandra limit in, 219
创建于223 年的元素
elements created in, 223
由221 号发射的能量
energy emitted by, 221
铁芯在，219
iron core in, 219
中微子，221-22
neutrinos in, 221–22
中子星，217，219-21
质子数，220-21
protons in, 220–21
残余，221
remnant of, 221
电晕放电，145
corona discharge, 145
在 X 射线气球中，206 –7
in X-ray ballooning, 206–7
宇宙距离阶梯，34
cosmic distance ladder, 34
cosmic microwave background (CMB) radiation, 9, 199
宇宙射线，230
cosmic rays, 230
查尔斯·奥古斯丁·库仑，133
Coulomb, Charles-Augustin de, 133
库仑（电荷单位），133
coulomb (unit of charge), 133
库仑定律，133-34
Coulomb’s law, 133–34
蟹状星云（ M - 1），192，196-97，221，242
Crab Nebula (M-1), 192, 196–97, 221, 242
形状的变化，222
changing shape of, 222
月掩星，197-98
Moon in occultation of, 197–98
脉冲星在，224 –25
pulsar in, 224–25
南十字座（星座），213
crux (constellation), 213
Crux X-1（X射线源），213
Crux X-1 (X-ray source), 213
居里，玛丽，268
Curie, Marie, 268
居里温度，152
Curie temperature, 152
回旋加速器，7
cyclotron, 7
Cyg X - 1（X射线源），196，212-13，234，240-42，245
Cyg X-1 (X-ray source), 196, 212–13, 234, 240–42, 245
天鹅座 X-2（X射线源），196
Cyg X-2 (X-ray source), 196
辛戈斯（星座），196
Cyngus (constellation), 196
托马斯·弗朗索瓦·达利巴，146
Dalibard, Thomas-François, 146
道尔顿，约翰，174
Dalton, John, 174
达尔文，查尔斯，34岁
Darwin, Charles, 34
分贝，105
decibels, 105
除颤器，142台
defibrillators, 142
德加，埃德加，267
Degas, Edgar, 267
简并中子物质，220
degenerate neutron matter, 220
德克斯，丹尼尔，265
Dekkers, Daniel, 265
Delft University of Technology, 1, 10–11
德谟克利特，189
Democritus, 189
德兰，安德烈，268
Derain, André, 268
相消干涉，95
destructive interference, 95
抗磁性材料，151
diamagnetic materials, 151
迪吉里杜管（乐器），120
didgeredoo (musical instrument), 120
衍射（干涉），95-96
diffraction (interference), 95–96
偶极子，165-66
dipoles, 165–66
狄拉克，保罗，269
Dirac, Paul, 269
直流电（DC），158
direct current (DC), 158
多普勒效应，232-33
Doppler effect, 232–33
在二进制系统中，237、238-39
in binary systems, 237, 238–39
黑洞和，232-33
black holes and, 232–33
恒星距离和，34 –35
stellar distances and, 34–35
X-ray binaries and, 237–39, 241, 243
双人跳绳（游戏），110
double-dutch (game), 110
《引雷而下：本杰明·富兰克林与启蒙时代的电气技术》（希弗出版社），第146页
Draw the Lightning Down: Benjamin Franklin and Electrical Technology in the Age of Enlightenment (Schiffer), 146
驱动振荡器，110
driven oscillator, 110
杜尚，马塞尔，268
Duchamp, Marcel, 268
发电机效应，153
dynamo effect, 153
地球，28，49，50-51，55，187，227，236，244，279
Earth, 28, 49, 50–51, 55, 187, 227, 236, 244, 279
年龄，36岁
age of, 36
平均半径为283
average radius of, 283
计算月球距离，282 –83
calculating distances to Moon from, 282–83
calculating mass of, 282–83, 284
核心，152-53，183
密度为284
density of, 284
重力加速度和，41-42
gravitational acceleration and, 41–42
磁场，9，152-53，154
magnetic field of, 9, 152–53, 154
质量为，45
mass of, 45
中微子继续撞击，222
neutrino strikes on, 222
太阳距离，181，281-82
Sun’s distance from, 181, 281–82
地表气压为：63-64，66-67
surface air pressure of, 63–64, 66–67
雷暴持续，143
thunderstorms on, 143
潮汐力作用，233
tidal forces on, 233
电压为137
voltage of, 137
e-Astronomer（博客），195
e-Astronomer (blog), 195
黄道面，29
ecliptic plane, 29
翁贝托·埃科，266
Eco, Umberto, 266
涡流，161
eddy currents, 161
爱因斯坦，阿尔伯特，9，19，21，38，165，166，167，226-227，228，268，269-270
Einstein, Albert, 9, 19, 21, 38, 165, 166, 167, 226–27, 228, 268, 269–70
在古希腊，126
in ancient Greece, 126
以原子计，130
in atoms, 130
吸引和排斥，128，132-36
attraction and repulsion and, 128, 132–36
化学反应和，129-30
chemical reactions and, 129–30
conductors and conduction in, 128–29, 132, 136
corona discharge and, 145, 206–7
库仑定律和，133-34
Coulomb’s law and, 133–34
早期科学研究，126
early scientific study of, 126
作为液体，128
as fluid, 128
Franklin’s experiments in, 128–29, 146–47
高斯定律，165
Gauss’s law for, 165
促进愈合刺激，以及，142
healing stimulation and, 142
在人体内，129
in human body, 129
归纳过程和，133-35
induction process and, 133–35
insulators and, 128–29, 131–32, 136
致死率，142-43
lethality of, 142–43
在闪电中，看到闪电
in lightning, see lightning
命名，126
naming of, 126
普遍性，129-30
pervasiveness of, 129–30
正电荷和负电荷，130 –31
positive and negative charges and, 130–31
短路和，142-43
short circuits and, 142–43
酷刑和，141
torture and, 141
摩擦电效应，127、132、135、140
triboelectric effect and, 127, 132, 135, 140
电动力悬浮（EDS），163
electrodynamic suspension (EDS), 163
电磁悬浮（EMS），163-64
electromagnetic suspension (EMS), 163–64
电磁学，36，39，166，167，227，232
electromagnetism, 36, 39, 166, 167, 227, 232
电子数：6、40、116、153、155、245
electrons, 6, 40, 116, 153, 155, 245
在核心坍缩超新星中，220 –21
in core-collapse supernova, 220–21
电流和，131-32
electric current and, 131–32
电场和，40
electric field and, 40
在磁性材料中，151
in magnetic materials, 151
负电荷，131
negative charge of, 131
“量化”，238
”quantized,” 238
尺寸为8
size of, 8
火花和，138
sparks and, 138
验电器，155
electroscope, 155
优雅的宇宙，（格林），23
Elegant Universe, The (Greene), 23
吸收线，237 –38
absorption lines of, 237–38
核衰变，7-8
nuclear decay of, 7–8
超新星及其形成，223
supernova and creation of, 223
伊丽莎白一世，英格兰女王，152年
Elizabeth I, Queen of England, 152
振幅和，105
amplitude and, 105
ATP 和，169
ATP and, 169
在体细胞中，169
in body cells, 169
化学，169-70
chemical, 169–70
在日常生活中，180
in everyday life, 180
食物，176-79
food, 176–79
全球变暖危机，以及，185-87
global warming crisis and, 185–87
引力势，参见引力势能
gravitational potential, see gravitational potential energy
热作为一种形式，174-75
heat as form of, 174–75
家庭使用量，180-81
household use of, 180–81
动力学 (KE), 154 , 170 , 171 –72, 173 , 176 , 179 , 221 , 246
kinetic (KE), 154, 170, 171–72, 173, 176, 179, 221, 246
雷击，144-45
of lightning stroke, 144–45
机械，173
mechanical, 173
运动，以及，参见运动，将能量转化为
motion and, see motion, converting energy into
核，183-85
nuclear, 183–85
核聚变和，186-87
nuclear fusion and, 186–87
身体活动和，177-79
physical activity and, 177–79
潜力，173
potential, 173
出自《快速爆发》，第256-57页
from Rapid Bursters, 256–57
太阳，181-82
solar, 181–82
来自星星，218
from stars, 218
单位，177
units for, 177
电压和，137
voltage and, 137
风力发电和，182-83
wind power and, 182–83
在X射线爆发中，249
in X-ray bursts, 249
X射线，191-92
of X-rays, 191–92
能量守恒，181
energy, conservation of, 181
课堂演示，168-69，173-74
classroom demonstrations of, 168–69, 173–74
能量转换，169-88
energy, conversion of, 169–88
课堂演示，170
classroom demonstrations of, 170
重力势能和，171-72
gravitational potential energy and, 171–72
焦耳的发现，174-75
Joule’s discovery of, 174–75
在核反应堆中，170
in nuclear reactors, 170
英格兰，127
England, 127
赤道坐标系，250
equatorial coordinate system, 250
尔格，177
ergs, 177
错误框，195
error box, 195
逃逸速度，227
escape velocity, 227
埃文斯，WD，248
Evans, W. D., 248
事件视界，226，228-29，231，232-34
event horizon, 226, 228–29, 231, 232–34
半径为228
radius of, 228
珠穆朗玛峰，山，64
Everest, Mount, 64
一切，理论，167
everything, theory of, 167
进化，34
evolution, 34
法拉第，迈克尔，156-57，166
费米，恩里科，269
Fermi, Enrico, 269
铁磁材料，156
ferromagnetic material, 156
铁磁性，150-51
ferromagnetism, 150–51
柴火，180
firewood, 180
费舍尔，菲利普，212-13
Fisher, Philip, 212–13
夸克的味，9
flavors, of quarks, 9
航班，73 –75
flight, 73–75
伯努利原理，73-74
Bernoulli principle and, 73–74
反作用力提升，74-75
reaction lift and, 74–75
长笛，119
flute, 119
食物，169
food, 169
食物能量，176-79
food energy, 176–79
Fortran（计算机语言），208
Fortran (computer language), 208
化石燃料，170、181、182、185
fossil fuel, 170, 181, 182, 185
法国，127
France, 127
核能，185
nuclear power in, 185
Franklin, Benjamin, 128, 130–31, 155
富兰克林，罗莎琳德，32岁
Franklin, Rosalind, 32n
频率：
frequency:
大爆炸，108-9
of big bang, 108–9
基本，110-11
fundamental, 110–11
谐波和，114-15
harmonics and, 114–15
摩擦力，39
friction, 39
机械能和，173
mechanical energy and, 173
另见空气阻力
see also air drag
弗里德曼，赫伯特，195，197-98，212，213
Friedman, Herbert, 195, 197–98, 212, 213
以及空间的扩张，18-19
and expansion of space, 18–19
长城，5
Great Wall of, 5
喷射物来自，199
jets emitted from, 199
测绘项目，108
mapping projects of, 108
英仙座星系团，108
Perseus cluster of, 108
血浆输入，107
plasma in, 107
伽利略·伽利雷, 25 –26, 27 , 42 , 43 , 50 , 51 , 66 , 126 , 172 , 189 , 278 , 282
Galileo Galilei, 25–26, 27, 42, 43, 50, 51, 66, 126, 172, 189, 278, 282
伽马射线，8、183、190、191、225
gamma rays, 8, 183, 190, 191, 225
从超新星中喷射而出，222-23
expelled from supernovae, 222–23
盖茨，比尔，x
Gates, Bill, x
高斯，卡尔·弗里德里希，156
Gauss, Carl Friedrich, 156
高斯电学定律，165
Gauss’s law for electricity, 165
高斯磁定律，165
Gauss’s law for magnetism, 165
盖斯勒，本杰明，99
Geisler, Benjamin, 99
广义相对论，理论，19，228，269-70
general relativity, theory of, 19, 228, 269–70
发电机，156-57，166
地磁暴，154
geomagnetic storms, 154
乔治二世，英格兰国王，147年
George II, King of England, 147
里卡多·贾科尼, 17 , 193 , 195 , 196 , 216 , 243
Giacconi, Riccardo, 17, 193, 195, 196, 216, 243
吉尔，大卫，30岁
Gill, David, 30
Glashow, Sheldon, 22, 116, 167
玻璃弓，99-102
glassbows, 99–102
全球变暖，185
global warming, 185
荣耀（布罗肯幽灵），97-98
glories (Brocken spectres), 97–98
戈达德太空飞行中心，251
Goddard Space Flight Center, 251
戈尔德，托马斯，225
Gold, Thomas, 225
古德斯米特，塞缪尔，215
Goudsmit, Samuel, 215
大统一理论，167
grand unified theory, 167
重力加速度，40-43，46-47
gravitational acceleration, 40–43, 46–47
万有引力常数，284
gravitational constant, 284
gravitational potential energy, 246, 256–57, 258
天文学和，172-73，174
动能和，171-72
kinetic energy and, 171–72
X射线暴，256-57，258
gravitational redshift, 227, 232–33
重力，24，39，45，55-58，167，171，270
gravity, 24, 39, 45, 55–58, 167, 171, 270
人工的，55-58
artificial, 55–58
向心力，以及，56-57
centripetal force and, 56–57
自由落体，47-48
free fall and, 47–48
静水压力和，71-73
hydrostatic pressure and, 71–73
时空和，226-27
spacetime and, 226–27
星星，218颗
of stars, 218
体重，41
weight and, 41
另见万有引力定律
see also universal law of gravitation
格雷，斯蒂芬，128-29
Gray, Stephen, 128–29
星系长城，5
Great Wall of galaxies, 5
Greece, ancient, 115, 126, 150
格林，布莱恩，23岁
Greene, Brian, 23
greenhouse gases, 164–65, 183, 186
绿色和平国际，182
Greenpeace International, 182
绿色条纹（马蒂斯），267
Green Stripe, The (Matisse), 267
格雷戈里，弗雷德里克，155
Gregory, Frederick, 155
格林德利，乔什，248，250，255，257
Grindlay, Josh, 248, 250, 255, 257
吉他，112，113，119
GX 1+4 (X-ray source), 201, 244
GX 301-2（X射线源），201
GX 301-2 (X-ray source), 201
GX 304-1（X射线源），201
GX 304-1 (X-ray source), 201
汉密尔顿，安德鲁，233
Hamilton, Andrew, 233
谐波：
harmonics:
共振和，111，114-16
弦乐器，114-15
in stringed instruments, 114–15
音叉，115-16
of tuning fork, 115–16
竖琴，112
harp, 112
哈佛大学，26-27
Harvard University, 26–27
霍金辐射，231
Hawking radiation, 231
海姆斯，鲍勃，200
Haymes, Bob, 200
HDE 226868（超巨星），240 –41
HDE 226868 (supergiant star), 240–41
热量，169
heat, 169
身体，176-77，179
作为能量形式，174-75
as form of energy, 174–75
在核电站中，184
in nuclear power plant, 184
恒星，218 –19
of stars, 218–19
海斯，约翰，248
Heise, John, 248
海森堡，维尔纳，268-69
Heisenberg, Werner, 268–69
在核心坍缩超新星中，218 –19
in core-collapse supernova, 218–19
在X射线气球中，203
in X-ray ballooning, 203
Hercules (constellation), 196, 243
赫兹，104
hertz, 104
赫茨普龙，埃纳尔，33
Hertzsprung, Ejnar, 33
Her X-1 (X-ray source), 196, 243
Hipparcos（高精度视差收集卫星），31
Hipparcos (High Precision Parallax Collecting Satellite), 31
霍夫曼，杰弗里，254-55
Hoffman, Jeffrey, 254–55
大屠杀，11-13
Holocaust, 11–13
同极马达，161
homopolar motor, 161
胡克，罗伯特，126
Hooke, Robert, 126
哈勃常数，35-36
Hubble’s constant, 35–36
哈勃定律，35
Hubble’s law, 35
哈勃太空望远镜，187-88，199，222，243
Hubble Space Telescope, 187–88, 199, 222, 243
Hubble Ultra Deep Field, 18, 260
赫尔西泽，罗伯特，十四至十五
Hulsizer, Robert, xiv–xv
洪堡，亚历山大·冯，236
Humboldt, Alexander von, 236
惠更斯，克里斯蒂安，126
Huygens, Christian, 126
《流体动力学（伯努利）》，73
Hydrodynamica (Bernoulli), 73
hydrogen, 6, 151, 238, 251, 256
吸收线，238
absorption lines of, 238
在核心坍缩超新星中，218 –19
in core-collapse supernova, 218–19
在核聚变中，186-87
in nuclear fusion, 186–87
在X射线双星系统中，246
in X-ray binary system, 246
静水压力，65-73
hydrostatic pressure, 65–73
重力，71-73
gravity and, 71–73
树木和，72-73
trees and, 72–73
伊本·海赛姆，79
Ibn al-Haytham, 79
冰，61
ice, 61
冰立方（望远镜），190
IceCube (telescope), 190
感应闪电，143
induction lightning, 143
惯性定律，38-39
inertia, law of, 38–39
红外辐射，104，176-77，190，192-93，232
infrared radiation, 104, 176–77, 190, 192–93, 232
绝缘体，128-29，131-32，136
insulators, 128–29, 131–32, 136
干涉（衍射），95-96
interference (diffraction), 95–96
星系际介质（等离子体），参见等离子体
intergalactic medium (plasma), see plasma
国际能源署，182
International Energy Agency, 182
互联网，x
Internet, x
行星际等离子体，参见太阳风
interplanetary plasma, see solar wind
离子，40，131，139
电流和，131
electric current and, 131
伊朗，183，184-85
铁，150 –51
iron, 150–51
在地球核心，152 –53
in Earth’s core, 152–53
在恒星核心中，219
in star cores, 219
iTunes U，x
iTunes U, x
英格兰国王詹姆斯一世，70
James I, King of England, 70
扬斯基，卡尔，190
Jansky, Karl, 190
詹克斯，查尔斯，266
Jencks, Charles, 266
喷射气流，204-5
jet stream, 204–5
犹太人，11-12
Jews, 11–12
约翰逊，BC，74
Johnson, B. C., 74
乔斯，保罗，256
Joss, Paul, 256
焦耳，詹姆斯，174-75
Joule, James, 174–75
焦耳（能量单位），137、174、175-76
joule (unit of energy), 137, 174, 175–76
《进入史瓦西黑洞之旅》（系列电影），233
“Journey into a Schwarzschild black hole” (film series), 233
JR磁悬浮列车，164
JR-Maglev train, 164
贾德，唐纳德，266
Judd, Donald, 266
木星（行星），49 –50，223 –24，279，281，282
Jupiter (planet), 49–50, 223–24, 279, 281, 282
月亮，189
moons of, 189
木星导弹，17
Jupiter missile, 17
康定斯基，瓦西里，268
Kandinsky, Wassily, 268
袋鼠杰克，210 –11
Kangaroo Jack, 210–11
考夫曼，苏珊，xiii，78，88，99，173-74，202
Kaufman, Susan, xiii, 78, 88, 99, 173–74, 202
肯尼亚，242
Kenya, 242
约翰内斯·开普勒，51、126、189、190、281
Kepler, Johannes, 51, 126, 189, 190, 281
开普勒定律，190
Kepler’s laws, 190
千卡，177
kilocalorie, 177
动能（KE ），154、170、173、176、179、221、246
kinetic energy (KE), 154, 170, 173, 176, 179, 221, 246
重力势能和，171-72
gravitational potential energy and, 171–72
柯达，205
Kodak, 205
库哈斯，雷姆，266
Koolhaas, Rem, 266
宇宙428号卫星，253
Kosmos 428 satellite, 253
拉格朗日点，244
Lagrangian point, 244
兰德，埃德温，92岁
Land, Edwin, 92
大额外维度理论，229-30
large extra dimensions, theory of, 229–30
Large Hadron Collider (LHC), 231, 260
以及黑洞的形成，229-30
and creation of black holes, 229–30
大麦哲伦星云，222-23
Large Magellanic Cloud, 222–23
劳伦斯，安迪，195
Lawrence, Andy, 195
利维特，亨丽埃塔·斯旺，31-32
Leavitt, Henrietta Swan, 31–32
Leeb，Steven，第十四页
Leeb, Steven, xiv
莱布尼茨，戈特弗里德，126
Leibniz, Gottfried, 126
Levitron，164
Levitron, 164
莱温，伊曼纽尔“查克” ，第十二卷，第十五卷，第十六卷，第十八六页
Lewin, Emanuel “Chuck,” xii, xv, 16, 186
莱文，古斯塔夫，11
Lewin, Gustav, 11
莱文，惠伯莎，2
Lewin, Huibertha, 2
莱文，雅各布，11-12
Lewin, Jacob, 11–12
莱文，雅各布，16岁
Lewin, Jakob, 16
莱文，朱莉娅，11-12
Lewin, Julia, 11–12
莱文，沃尔特，老，13-16
Lewin, Walter, Sr., 13–16
莱文，沃尔特·HG：
Lewin, Walter H. G.:
艺术合作，263，264-67
art collaborations of, 263, 264–67
艺术收藏品，262
art collection of, 262
出生日期，11
birth of, 11
职业生涯，十三至十四
career of, xiii–xiv
早期教育，1-2
early education of, 1–2
《纽约时报》关于x 的文章
New York Times piece on, x
教学风格，xi –xii ，xiv，xv，263，270 –71
teaching style of, xi–xii, xiv, xv, 263, 270–71
university education of, 10–11, 16
第二次世界大战经历，11-16
World War II experience of, 11–16
莱文·戈特菲尔德，艾玛，11岁
Lewin Gottfeld, Emma, 11
莱顿瓶，155
Leyden jars, 155
LGM-1（脉冲星），225
LGM-1 (pulsar), 225
利克天文台，196 -97年
Lick Observatory, 196–97
连，265
Lien, 265
《美丽人生》（电影），12
Life Is Beautiful (film), 12
轻，225
light, 225
极光和，153
auroras and, 153
黑洞和速度，232
black holes and speed of, 232
在暗箱中，78-79
in camera obscura, 78–79
作为电磁波，166
as electromagnetic wave, 166
在牛顿棱镜实验中，80
in Newton’s prism experiment, 80
极化，91-93
polarized, 91–93
折射，80-82
refraction of, 80–82
火花，139
of sparks, 139
在分束实验中，94-95
in split-beam experiment, 94–95
波长为104
wavelength of, 104
X射线和，191-92
X-rays and, 191–92
灯塔效应，225
lighthouse effect, 225
光线实验，263
Light Line Experiment, 263
蓝色喷气式飞机，148
blue jet form of, 148
距离为144
distance of, 144
电流输入，138-39，141，143-44
electric current in, 138–39, 141, 143–44
电场和，137-38
electric fields and, 137–38
电击，138-39
electric shock of, 138–39
释放的能量，144 –45
energy released by, 144–45
出现频率为143
frequency of occurence of, 143
在高海拔地区，147-48
at high altitudes, 147–48
避雷针和，147
lightning rods and, 147
最大功率为144
maximum power of, 144
在神话中，143
in mythology, 143
臭氧和，144-45
ozone and, 144–45
红色精灵形态，148
red sprite form of, 148
火花和，138-41
sparks and, 138–41
电压和，137 –38
voltage and, 137–38
光行时间距离，35
light travel time distance, 35
线性偏振器，92
linear polarizer, 92
液体，压力，参见静水压力
liquids, pressure in, see hydrostatic pressure
洛克希德导弹与航天公司，212
Lockheed Missiles and Space Company, 212
磁石，150
lodestones, 150
“从物理学家的视角看20世纪艺术”，267
“Looking at 20th-Century Art Through the Eyes of a Physicist,” 267
洛斯阿拉莫斯国家实验室，258-59
Los Alamos National Laboratory, 258–59
亮度：
luminosity:
亮度，32-33
brightness and, 32–33
在造父变星中，32 –34
in Cepheid variables, 32–34
X射线，246
of X-rays, 246
M-1，参见蟹状星云
M-1, see Crab Nebula
M31，参见仙女座星系
M31, see Andromeda galaxy
McClintock, Jeff, 211 –12, 234 , 242 , 254 , 255
McClintock, Jeff, 211–12, 234, 242, 254, 255
磁悬浮列车，162-65
maglev trains, 162–65
镁，151
magnesium, 151
Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, De（论磁铁和磁性体，以及论地球大磁铁）（吉尔伯特），152、155
Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, De(On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth) (Gilbert), 152, 155
磁轫致辐射，192
magnetic bremsstrahlung, 192
磁力，39
magnetic force, 39
magnetism, magnetic fields, 149–67, 261
在古代，150
in ancient era, 150
在动物中，152
in animals, 152
极光和，153-54
auroras and, 153–54
抗磁性材料和，151
diamagnetic materials and, 151
地球，152-53
of Earth, 152–53
电磁学，154-57
electromagnetism and, 154–57
铁和，150-51
iron and, 150–51
液体，151
liquid, 151
在磁悬浮列车中，162 –65
in maglev trains, 162–65
麦克斯韦方程组和，165
Maxwell’s equations and, 165
在迁徙鸟类中，152
in migrating birds, 152
单极子和，165
monopoles and, 165
中子星，224
of neutron star, 224
顺磁性材料和，151
paramagnetic materials and, 151
太阳风和，153-54
solar wind and, 153–54
太阳报，153
of Sun, 153
超导体和，163
superconductors and, 163
电视机，149-50
in television sets, 149–50
以及万物理论，167
and theory of everything, 167
磁铁矿（氧化铁），150
magnetite (iron oxide), 150
哺乳动物股骨，25-27，26，277-78
mammalian femurs, 25–27, 26, 277–78
马拉斯基，劳拉，251-52
Maraschi, Laura, 251–52
氛围，154
atmosphere of, 154
磁场强度为154
magnetic field of, 154
火星气候轨道器，22
Mars Climate Orbiter, 22
马歇尔，赫尔曼，255
Marshall, Herman, 255
马歇尔太空飞行中心，17
Marshall Space Flight Center, 17
计算结果为281 – 84
calculating, 281–84
地球，45
of Earth, 45
普朗克，230
Planck, 230
质子数，229
of protons, 229
太阳报，279
of Sun, 279
麻省理工学院（MIT ），ix，xiv，10，11，18，214
Massachusetts Institute of Technology (MIT), ix, xiv, 10, 11, 18, 214
马蒂斯，亨利，267-68
Matisse, Henri, 267–68
在黑洞中，225-26
in black holes, 225–26
在二元系统中，流量为244 –45
flow of, in binary systems, 244–45
夸克和，9
quarks and, 9
在太空中，107
in space, 107
以及振动的弦，116
and vibrating strings, 116
X射线加热，192
X-ray heating of, 192
Maxwell ， James Clerk，156，165-67，261
Maxwell, James Clerk, 156, 165–67, 261
麦克斯韦方程组，165-67，270
Maxwell’s equations, 165–67, 270
梅奥尔，尼古拉斯，196 -97年
Mayall, Nicholas, 196–97
measurements, measuring, ix, 21–36
气压，61-63
air pressure, 61–63
天文学和，27-28
astronomy and, 27–28
and degree of accuracy, 8, 23–25
闪电距离，144
distance of lightning, 144
电流，141
electrical current, 141
星际空间，参见恒星距离，测量
of interstellar space, see stellar distances, measurement of
哺乳动物股骨，25-27，26，277-78
of mammalian femur, 25–27, 26, 277–78
静电，155
static electricity, 155
以及万有引力定律，49-51
and universal law of gravitation, 49–51
机械能，173
mechanical energy, 173
兆秒差距，35
megaparsec, 35
梅特纳，莉丝，32岁
Meitner, Lise, 32n
mercury (element), 7, 66–67, 151
梅西耶，查尔斯，196
Messier, Charles, 196
Messier 产品目录，196 年
Messier catalog, 196
陨石，4
meteorites, 4
米歇尔，约翰，228
Michell, John, 228
微型黑洞，229-31
micro black holes, 229–31
显微镜，130
microscopes, 130
微波辐射，190
microwave radiation, 190
银河系，2，5，33，203
Milky Way galaxy, 2, 5, 33, 203
190 年的无线电波发射
radio wave emissions in, 190
千禧桥，124
Millennium Bridge, 124
米勒，乔恩，234
Miller, Jon, 234
麻省理工学院世界，134
MIT World, 134
蒙德里安，皮特，265-66，268
单极子，165-66
monopoles, 165–66
梦露，玛丽莲，268
Monroe, Marilyn, 268
月亮，3，17，41，49，50-51，227，233，236，244
Moon, 3, 17, 41, 49, 50–51, 227, 233, 236, 244
角尺寸为30
angular size of, 30
计算距离，282 – 83
calculating distance of, 282–83
重力加速度为172
gravitational acceleration of, 172
引力以及，39
gravitational attraction and, 39
蟹状星云掩星，197-98
in occultation of Crab Nebula, 197–98
真空状态下，107
as vacuum, 107
193 -94年的X射线
X-rays from, 193–94
运动，将能量转化为：
motion, converting energy into:
悬浮演示，161-62
levitation demonstration of, 161–62
电机和，157，159-61
另见牛顿定律
see also Newton’s laws
电机，157
motors, 157
建筑，159 –61
building, 159–61
同极性，161
homopolar, 161
莫扎特，沃尔夫冈·阿玛多伊斯，117
Mozart, Wolfgang Amadeus, 117
M理论，23
M-theory, 23
默丁，保罗，241-42
Murdin, Paul, 241–42
音乐，103
music, 103
谐波输入，114
harmonics in, 114
MXB 1636-53（X射线源），254-55，257
MXB 1636-53 (X-ray source), 254–55, 257
MXB 1659-29（X射线源），250
MXB 1659-29 (X-ray source), 250
MXB 1730-335 （X射线源），252-53
MXB 1730-335 (X-ray source), 252–53
MXB 1735-44 （X射线源），254-55
MXB 1735-44 (X-ray source), 254–55
纳米，105
nanometers, 105
拿破仑一世，法兰西皇帝，141年
Napoleon I, Emperor of France, 141
美国国家航空航天局（ NASA ），17、24、99、193、202、206、213、251、258
NASA (National Aeronautics and Space Administration), 17, 24, 99, 193, 202, 206, 213, 251, 258
美国国家科学基金会，203
National Science Foundation, 203
自然哲学，126
natural philosophy, 126
自然选择，34
natural selection, 34
海军研究实验室，195
Naval Research Laboratory, 195
霓虹灯，219
neon, 219
荷兰，1，10，155，158，201
Netherlands, 1, 10, 155, 158, 201
热能，221
thermal, 221
中微子望远镜，190
neutrino telescopes, 190
中子，9，130，197，220-21
在核心坍缩超新星中，221 –22
in core-collapse supernova, 221–22
在血浆中，107
in plasma, 107
中子星，172-73，192，226，230，235，251，257
neutron stars, 172–73, 192, 226, 230, 235, 251, 257
in binary systems, 239–40, 242–45
in core-collapse supernova, 217, 219–21
蟹状星云，224
of Crab Nebula, 224
发现，217
discovery of, 217
灯塔效应，225
lighthouse effect of, 225
磁场强度为224
magnetic field of, 224
磁极数为245
magnetic poles of, 245
作为脉冲星，224-25
as pulsars, 224–25
旋转，224 –25
rotation of, 224–25
大小为223 –24
size of, 223–24
supernova and, 197, 217–20, 221
表面温度为217
surface temperature of, 217
X射线加热，246
X-ray heating of, 246
新一代能源，186
New Generation Energy, 186
牛顿，艾萨克，第十四卷，第9、21、39、41、44、48、49-50、58、79、94、126、146、165、166、189、244、261、268、280、284页
Newton, Isaac, xiv, 9, 21, 39, 41, 44, 48, 49–50, 58, 79, 94, 126, 146, 165, 166, 189, 244, 261, 268, 280, 284
光棱镜，80
light prism of, 80
牛顿（力的单位），40
newton (unit of force), 40
牛顿定律，38-48、58、172、269
Newton’s laws, 38–48, 58, 172, 269
计算地球与月球之间的距离，282 –83
calculating distance between Earth and Moon with, 282–83
计算质量，281 –84
calculating mass with, 281–84
计算轨道周期，279 –81
calculating orbital periods with, 279–81
first (law of inertia), 38–39, 51
自由落体，47-48
free fall and, 47–48
重力加速度和，40-43
gravitational acceleration and, 40–43
影响，50-51
impact of, 50–51
第二（力的计算），39-43，46
second (calculation of force), 39–43, 46
third (acceleration), 46–48, 56
以及万有引力定律，49-51
and universal law of gravitation, 49–51
失重状态，47-48
weightlessness and, 47–48
纽约州纽约市，72
New York, N.Y., 72
纽约时报，x
New York Times, x
镍，151
nickel, 151
氮，153
nitrogen, 153
节点，111
nodes, 111
nonconductors, 128–29, 131–32, 136
诺尔玛（星座），195
Norma (constellation), 195
北极光（极光），10，153-54，245
northern lights (aurora borealis), 10, 153–54, 245
音符配对，114
note-pairing, 114
核衰变，7-8
nuclear decay, 7–8
核能，183-85
nuclear energy, 183–85
nuclear fission, 183–85, 186–87, 218
核聚变，186-87，188，219，223，251
nuclear fusion, 186–87, 188, 219, 223, 251
星星数量：218
in stars, 218
核反应堆，170，183-85
掩星，197
occultation, 197
八度，114
octaves, 114
石油禁运，181
oil embargo, 181
1972年奥运会，264
Olympic Games of 1972, 264
奥尔特，201-2年1 月
Oort, Jan, 201–2
欧佩克（石油输出国组织），181
OPEC (Organization of Petroleum Exporting Countries), 181
光学（牛顿），80
Opticks (Newton), 80
轨道平面，29
orbital plane, 29
猎户座（星座），237
Orion (constellation), 237
奥罗斯，杰瑞，242
Orosz, Jerry, 242
汉斯·克里斯蒂安·奥斯特德，155 –56
Ørsted, Hans Christian, 155–56
Ørsted卫星，153
Ørsted satellite, 153
奥弗贝克，吉姆，200
Overbeck, Jim, 200
泛音，112
overtones, 112
oxygen, 6–7, 107, 151, 153, 219
在磁铁矿中，150
in magnetite, 150
臭氧和，144-45
ozone and, 144–45
桨轮，174 –75
paddle wheel, 174–75
白南准，150
Paik, Nam June, 150
视差，28-31，33，34，36
视差角，28–30
parallax angle, 28–30
顺磁性材料，151
paramagnetic materials, 151
保利，沃尔夫冈，268
Pauli, Wolfgang, 268
PBS，23
PBS, 23
佩德森，霍尔格，257
Pederson, Holger, 257
摆锤，52-55
pendulums, 52–55
空气阻力（摩擦力）和，52
air drag (friction) and, 52
能量守恒，168-69，173-74
conservation of energy and, 168–69, 173–74
时期，52，54-55，106
英仙座星系团，108
Perseus cluster, 108
彼得森，拉里，200
Peterson, Larry, 200
光电吸收，207
photoelectric absorption, 207
《物理评论快报》，215
Physical Review Letters, 215
物理学，5-6，50，261，262
作为自然哲学，126
as natural philosophy, 126
先驱者，268
pioneers of, 268
钢琴，112，113，114，116
毕加索，巴勃罗，268
Picasso, Pablo, 268
短笛，120
piccolo, 120
管风琴，120 –21
pipe organ, 120–21
毕沙罗，卡米尔，267
Pissarro, Camille, 267
普朗克，马克斯，268
Planck, Max, 268
普朗克质量，230
Planck mass, 230
等离子体（星系际介质）：
plasma (intergalactic medium):
电离，131
ionization of, 131
声波，107 –8
sound waves of, 107–8
铂金，7
platinum, 7
冥王星，55
Pluto, 55
北极星，152
Polaris, 152
宝丽来公司，92
Polaroid Corporation, 92
波洛克，杰克逊，268
Pollock, Jackson, 268
波利，大卫，第十四
Pooley, David, xiv
钾-40，183
potassium-40, 183
势能，173
potential energy, 173
压力，59-77
pressure, 59–77
空气，参见气压
air, see air pressure
定义，61
definition of, 61
方向和，61-62
direction and, 61–62
航班和，73-75
flight and, 73–75
水静力学，63-73
hydrostatic, 63–73
中子简并度，220
neutron degeneracy, 220
吸管和，63-66
straws and, 63–66
水下，67-71
under water, 67–71
普里斯特利，约瑟夫，146
Priestley, Joseph, 146
《自然哲学的数学原理》（牛顿），50
Principia (Newton), 50
身为物理学家的特权（魏斯科普夫），19
Privilege of Being a Physicist, The (Weisskopf), 19
始祖，220
progenitor, 220
质子数：6、9、40、130、153、245
protons, 6, 9, 40, 130, 153, 245
在核心坍缩超新星中，220 –21
in core-collapse supernova, 220–21
质量为229
mass of, 229
在血浆中，107
in plasma, 107
比邻星，30
Proxima Centauri, 30
在蟹状星云中，224-25
in Crab Nebula, 224–25
毕达哥拉斯，115
Pythagoras, 115
quasars (quasi-stellar radio sources), 9, 199
射电望远镜，187
radio telescopes, 187
来自天鹅座 X- 1，240
from Cyg X-1, 240
发现，190
discovery of, 190
彩虹气球，奥运会，264
Rainbow balloon, Olympics, 264
彩虹，78-100，237
antisolar point of, 84, 89, 97
弧形，83
arc shape of, 83
常见程度，80
commonness of, 80
conditions for seeing, 81–82, 84
双倍，86
double, 86
结束，89
end of, 89
在喷泉中，88-89
in fountains, 88–89
玻璃珠，99-102
glass beads and, 99–102
荣耀和，97-98
glories and, 97–98
自制，86-88，87
homemade, 86–88, 87
寻找，84-85
hunting for, 84–85
干涉（衍射）和，95-96
interference (diffraction) and, 95–96
最大角度为，82 –83，82
maximum angles for, 82–83, 82
在神话中，80
in mythology, 80
在海浪中，85
in ocean waves, 85
在手中，90-91
in one’s hand, 90–91
起源于80 –81年
origins of, 80–81
polarization of light and, 91–93, 103
折射和，80-83，82
refraction and, 80–83, 82
三级，89
tertiary, 89
白色，96
white, 96
Rapid Bursters, 252–53, 255–59, 256
编目，258
cataloging of, 258
磁盘不稳定和，258
disk instability and, 258
由256 –57释放的能量
energy emitted by, 256–57
国家安全问题，以及，258-59
national security issue and, 258–59
另见X 射线暴
see also X-ray bursts
瑞利散射，3-4
Rayleigh scattering, 3–4
反作用力提升，74-75
reaction lift, 74–75
《真实纸张》，第257期
Real Paper, The, 257
录音机（乐器），119
recorder (instrument), 119
红移，237，238-39
另见多普勒效应
see also Doppler effect
红色精灵照明，147-48
red sprites lighting, 147–48
红石导弹，17
Redstone missile, 17
簧片乐器，120
reed instruments, 120
文艺复兴，269
Renaissance, 269
雷诺阿，皮埃尔-奥古斯特，267
Renoir, Pierre-Auguste, 267
共振，109-24
resonance, 109–24
在汽车中，117
in cars, 117
克拉尼板，118-19
Chladni plates and, 118–19
定义，109
definition of, 109
谐波和，111，114-16
侧向，124
lateral, 124
节点和，111
nodes and, 111
共振频率和，109 –12
resonance frequency and, 109–12
歌手和，116
singers and, 116
弦乐器，111-13
in stringed instruments, 111–13
弦理论和，116-17
string theory and, 116–17
超级，117 –18
super, 117–18
在悬索桥事故中，123-24
in suspension bridge disasters, 123–24
旋转叉，109-10
of turning fork, 109–10
以及震动的酒杯，118
and vibrating wineglass, 118
旋转管和，122-23
whirling tubes and, 122–23
共振吸收，238
resonance absorption, 238
里奇曼，格奥尔格·威廉，146-47
Richmann, Georg Wilhelm, 146–47
里克，乔治，211-12
Ricker, George, 211–12
伦琴，威廉，191
Röntgen, Wilhelm, 191
绳子，110 –11
rope, 110–11
布鲁诺·罗西, 10 , 16 –18, 107 , 193 , 195 , 199 , 201 , 215
Rossi, Bruno, 10, 16–18, 107, 193, 195, 199, 201, 215
扶轮社，211
Rotary Club, 211
Rotor (amusement park ride), 56–58, 136
皇家学会，146
Royal Society, 146
拉姆斯菲尔德，唐纳德，31岁
Rumsfeld, Donald, 31
萨格迪耶夫，罗尔德，253-54
Sagdeev, Roald, 253–54
圣彼得堡科学院，146
St. Petersburg Academy of Sciences, 146
萨拉姆，阿卜杜斯，167
Salam, Abdus, 167
桑德奇，艾伦，240
Sandage, Allan, 240
桑福德，比尔，162
Sanford, Bil, 162
SAS - 3（第三颗小型天文卫星），248-49，253，254，256，258，259
SAS-3 (Third Small Astronomy Satellite), 248–49, 253, 254, 256, 258, 259
卫星，153颗
satellites, 153
另请参阅特定卫星。
see also specific satellites
土星（火箭），17
Saturn (rocket), 17
萨克斯管，120
saxophone, 120
Scarlett ，Bob，258-59
Scarlett, Bob, 258–59
薛定谔，埃尔温，268
Schrödinger, Erwin, 268
史瓦西尔德，卡尔，228
Schwarzschild, Karl, 228
史瓦西半径，228
Schwarzschild radius, 228
《科学美国人》，182
Scientific American, 182
天蝎座（星座），195
Scorpio (constellation), 195
斯科特，大卫，42岁
Scott, David, 42
Sco X - 1 （ X射线源），31，195-96，198，201，247，248
Sco X-1 (X-ray source), 31, 195–96, 198, 201, 247, 248
发现来自213 –16的 X 射线通量
discovery of X-ray flux from, 213–16
Shklovsky model and, 239–40, 243
上海磁悬浮列车，164
Shanghai Maglev Train, 164
沙普利，哈洛，33岁
Shapley, Harlow, 33
Shift（Struycken），266
Shift (Struycken), 266
Shklovsky, Joseph, 239 –40, 243 , 253
Shklovsky, Joseph, 239–40, 243, 253
短路，142-43
short circuits, 142–43
硅，219
silicon, 219
天狼星，31
Sirius, 31
A，236
A, 236
B ，236-37，241
西塔琴，115
sitar, 115
皮肤效应，145-46
skin effect, 145–46
天空实验室，24
Skylab, 24
Sloan Digital Sky Survey (SDSS), 5, 108
《贫民窟的百万富翁》（电影），141
Slumdog Millionaire (film), 141
小角度近似，53
small-angle approximation, 53
Small Magellanic Cloud (SMC), 32, 33
浮潜用具，浮潜，67-70
snorkels, snorkeling, 67–70
碘化钠晶体，207
sodium iodide crystals, 207
日食，79
solar eclipse, 79
太阳能，181-82
solar energy, 181–82
太阳风，10，107，194
极光和，153-54
auroras and, 153–54
《沃尔特·莱文的一些最佳台词》（视频），第十二页
“Some of Walter Lewin’s Best Lines” (video), xii
声音，声波，92
sound, sound waves, 92
振幅为，104 –6
amplitude of, 104–6
来自黑洞，108
from black hole, 108
基本特征，104
fundamental character of, 104
强度为105
intensity of, 105
音调和，105
pitch and, 105
血浆和，107-8
plasma and, 107–8
共振，参见共振
resonance and, see resonance
在太空中，107 –9
in space, 107–9
波长为104 –5
wavelength of, 104–5
南十字星，213
southern cross, 213
南极光（aurora australis），153-54
southern lights (aurora australis), 153–54
声波输入，107-9
sound waves in, 107–9
检测到的X射线位于：17-18、187-88、199、200-201
X-rays detected in, 17–18, 187–88, 199, 200–201
苏联空间研究所，253
Space Research Institute, Soviet, 253
时空，269
spacetime, 269
重力和，226-27
gravity and, 226–27
意大利面化，233-34
spaghettification, 233–34
火花，206-7
sparks, 206–7
电子和，138
electrons and, 138
闪电和，138-41
lightning and, 138–41
噪音，139
noise of, 139
special relativity, theory of, 19, 269
光谱：
spectrum:
吸收线，237 –39
absorption lines of, 237–39
250具黑人尸体
of black bodies, 250
标准大气压，61
standard atmosphere, 61
标准蜡烛图，34
standard candles, 34
星团，51
star clusters, 51
星夜（梵高），267
Starry Night (van Gogh), 267
亮度和光度，32-33
brightness and luminosity of, 32–33
核心压力为218
core pressure of, 218
由218产生的能量
energy generated by, 218
由218产生的重力
gravity generated by, 218
热度，218 –19
heat of, 218–19
测量距离，参见恒星距离，测量
measuring distance of, see stellar distances, measurement of
核聚变，218
nuclear fusion in, 218
作为标准蜡烛图，34
as standard candle, 34
白矮星，230、241、244、245
white dwarf, 230, 241, 244, 245
另见造父变星；特定恒星
see also Cepheid variables; specific stars
静电，125-28
static electricity, 125–28
斯坦因，利奥，267-68
Stein, Leo, 267–68
恒星距离，测量：
stellar distances, measurement of:
Cepheid variables and, 32–34, 36
多普勒效应，34-35
Doppler effect and, 34–35
天文学的发展，27-28
evolution of astronomy and, 27–28
宇宙膨胀，以及，34-35
expansion of the universe and, 34–35
哈勃常数，35-36
Hubble’s constant and, 35–36
视差和，28-31，34，36
标准蜡烛图，34
standard candles and, 34
系统误差和，31
systematic error and, 31
恒星级黑洞，234
stellar-mass black holes, 234
恒星自转，220
stellar rotation, 220
斯蒂伯，南希，十三
Stieber, Nancy, xiii
斯特拉迪瓦里家族，114
Stradivarius family, 114
吸管，63-66
straws, 63–66
弦乐器，111-15
stringed instruments, 111–15
颜色（音色），112
color (timbre) of, 112
谐波和，114-15
harmonics and, 114–15
响度为，112 –13
loudness of, 112–13
泛音和，112
overtones and, 112
共振频率和，11-13
resonanace frequency and, 11–13
共鸣弦和，115
sympathetic strings and, 115
弦理论，22-23
string theory, 22–23
共振和，116-17
resonance and, 116–17
强核力，9、18、36、167
strong nuclear force, 9, 18, 36, 167
斯特鲁伊肯，彼得，264-67
Struycken, Peter, 264–67
斯图克利，威廉，49岁
Stukeley, William, 49
潜艇，70 -71年
submarines, 70–71
星期日，3、5、10、28、33、49-50、57、227
Sun, 3, 5, 10, 28, 33, 49–50, 57, 227
核心温度为218
core temperature of, 218
地球距离，181，281-82
Earth’s distance from, 181, 281–82
磁场强度为153
magnetic field of, 153
质量为279
mass of, 279
太阳耀斑，154次
solar flares of, 154
X-ray radiation from, 192–93, 194
太阳镜，91-92
sunglasses, 91–92
苏尼亚耶夫，拉希德，253
Sunyaev, Rashid, 253
超导体，163
superconductors, 163
超新星 1987A，222 –23
Supernova 1987A, 222–23
supernovas, xiv, 192, 196–97, 217
核心坍缩，参见核心坍缩超新星
core-collapse, see core-collapse supernova
来自223 号的 X 射线
X-rays from, 223
超弦理论，22
superstring theory, 22
斯旺克，简，251
Swank, Jean, 251
同步辐射，192
synchrotron radiation, 192
系统误差，31
systemic error, 31
塔科马海峡大桥，123
Tacoma Narrows Bridge, 123
金牛座（星座），196
Taurus (constellation), 196
Tau X-1（X射线源），196
Tau X-1 (X-ray source), 196
IceCube，190
IceCube, 190
中微子，190
neutrino, 190
收音机，187
radio, 187
X射线气球效应，204，206-8，209-11
in X-ray ballooning, 204, 206–8, 209–11
特勒夫森，克里斯蒂安娜，258
Tellefson, Christiane, 258
theory of everything, 22, 116, 167
热中微子，221
thermal neutrinos, 221
第三颗小型天文卫星（SAS - 3），248-49，253，254，256，258，259
Third Small Astronomy Satellite (SAS-3), 248–49, 253, 254, 256, 258, 259
索恩，基普，242
Thorne, Kip, 242
索尔索斯，特里，214
Thorsos, Terry, 214
三里岛，185
Three Mile Island, 185
音色（颜色），112
timbre (color), 112
扭矩，157 –58
torque, 157–58
逆转，159
reversal of, 159
伊万杰利斯塔·托里拆利，66 –67
Torricelli, Evangelista, 66–67
树木，72-73
trees, 72–73
摩擦电系列，127、132、135、140
triboelectric series, 127, 132, 135, 140
对流层顶，204
tropopause, 204
小号，112
trumpet, 112
大号，121
tuba, 121
钨，151
tungsten, 151
音叉，104
tuning fork, 104
振幅和频率为106
amplitude and frequency of, 106
频率为，106，109-10
谐波和，115 –16
harmonics and, 115–16
两度视场（2dF）星系红移巡天，108
Two-degree Field (2dF) Galaxy Redshift Survey, 108
不明飞行物，209
UFOs, 209
紫外线辐射，190、191、192、222-23
ultraviolet radiation, 190, 191, 192, 222–23
不确定性原理，269
uncertainty principle, 269
统一场论，166-67，270
unified field theory, 166–67, 270
universal law of gravitation, 49–51, 133
万有引力常数，50
gravitational constant and, 50
影响，50-51
impact of, 50–51
宇宙，28，187，188
宇宙大爆炸理论，参见宇宙大爆炸理论
big bang and, see big bang, theory of
扩展，34-35
expansion of, 34–35
尺寸为5
size of, 5
弦理论和，116-17
string theory and, 116–17
富集，184
enriched, 184
V-2火箭，16 -17年
V-2 rockets, 16–17
范艾伦辐射带，9
Van Allen belts, 9
范德格拉夫发电机，140 –41
Van de Graaff generator, 140–41
范·德雷贝尔，科内利斯，70岁
van Drebbel, Cornelis, 70
Van Gogh, Vincent, 263, 267, 268
Vela-5间谍卫星，248
Vela-5 spy satellites, 248
小提琴，112、113、114、115、119
violin, 112, 113, 114, 115, 119
声带，116
vocal cords, 116
伏特，137-38
volt, 137–38
定义，137
definition of, 137
伏特，亚历山德罗，138
Volta, Alessandro, 138
冯·布劳恩，沃纳，17
von Braun, Wernher, 17
威尔士，卡尔，96岁
Wales, Carl, 96
瓦普斯特拉，阿尔德特，7-8
Wapstra, Aaldert, 7–8
沃霍尔，安迪，268
Warhol, Andy, 268
华盛顿，芒特，66
Washington, Mount, 66
水，151
water, 151
作为指挥，132
as conductor, 132
电离，131
ionized, 131
在核电站中，184
in nuclear power plants, 184
瀑布，174-75
waterfalls, 174–75
瓦特（单位），177
watt (unit), 177
波长：
wavelength:
大爆炸，108-9
of big bang, 108–9
声波，104 –5
of sound waves, 104–5
W玻色子，18
W bosons, 18
weak nuclear force, 18, 38, 167
韦伯斯特，路易丝，241-42
Webster, Louise, 241–42
重量：
weight:
重力，以及41
gravity and, 41
摆锤，52
of pendulum, 52
weightlessness, 47–48, 56, 58, 65
温伯格，史蒂文，167
Weinberg, Steven, 167
白矮星，230、241、244、245
white dwarf stars, 230, 241, 244, 245
惠特尔，马克，109
Whittle, Mark, 109
谁害怕弗吉尼亚·伍尔夫？（阿尔比），123
Who’s Afraid of Virginia Woolf? (Albee), 123
风速，64
wind, 64
管乐器：
wind instruments:
基频为120
fundamental frequency of, 120
种类，119
kinds of, 119
以及空气柱长度，119-21、122、123
and length of air column, 119–21, 122, 123
风车，183
windmills, 183
风力发电，182-83
wind power, 182–83
威滕，爱德华，23岁
Witten, Edward, 23
戴帽子的女人（马蒂斯），267-68
Woman with a Hat (Matisse), 267–68
《电磁奇观》，134
“Wonders of Electricity and Magnetism, The,” 134
伍斯利，斯坦，223
Woosley, Stan, 223
第二次世界大战，11 -16年
World War II, 11–16
V-2火箭发射，16 -17年
V-2 rockets in, 16–17
X-ray astronomy, 187, 190–91, 193–99
生于193 -96年
birth of, 193–96
蟹状星云，196-97
Crab Nebula and, 196–97
增长，201-2
growth of, 201–2
卫星观测和，242-44
satellite observation and, 242–44
X射线气球，200-216
X-ray ballooning, 200–216
海拔高度，200
altitudes in, 200
电晕放电问题，206-7
corona discharge problem in, 206–7
发现于，212-16
discoveries in, 212–16
航班时长，200
duration of flights in, 200
失败次数，205-6
failures in, 205–6
基础设施，203
infrastructure for, 203
于203 –6年推出
launches in, 203–6
恢复情况，209 –11
recovery in, 209–11
基于火箭的探测和，200-201
rocket-based detection and, 200–201
望远镜，204，206-8，209-11
telescope in, 204, 206–8, 209–11
今天，206
today, 206
追踪结果，208 –10
tracking in, 208–10
天气和，204-5
weather and, 204–5
X射线双星：
X-ray binaries:
吸积中子星，239-40，241
accreting neutron star in, 239–40, 241
吸积盘，245 –46
accretion disk of, 245–46
黑体辐射和，246
blackbody radiation and, 246
黑洞，241-42，244
质心为，235 –36
center of mass of, 235–36
发现，241-42
discovery of, 241–42
Doppler effect and, 237–39, 241, 243
物质流入，244-45
flow of matter in, 244–45
朗格朗日点和，244
Langrangian point and, 244
radio jets from, 246
什克洛夫斯基模型，239-40，243
Shklovsky model of, 239–40, 243
光谱和，237-38
spectra and, 237–38
光谱学和，237-39
spectroscopy and, 237–39
视觉确认，236
visual confirmation of, 236
X-ray emissions from, 242–44, 246–47
X射线暴，xiv，247，248-57
X-ray bursts, xiv, 247, 248–57
黑色的尸体，以及，250-51
black bodies and, 250–51
黑洞和，257
black holes and, 257
“burst watch” 适用于254 –55
”burst watch” for, 254–55
原因，250
causes of, 250
发现，248-49
discovery of, 248–49
gravitational potential energy of, 256–57, 258
如快速爆发，请参阅快速爆发。
as Rapid Bursters, see Rapid Bursters
规律性，249-50
regularity of, 249–50
来源，251
sources of, 251
苏联的侦测，253-54
Soviet detection of, 253–54
热核模型，251-53，256
thermonuclear model of, 251–53, 256
I 型，256 –57
Type I, 256–57
II 型，256 –57
Type II, 256–57
X射线能量，249
X-ray energy in, 249
X射线加热，246
X-ray heating, 246
X射线，xiv，10，16，17，21-22，225
X-rays, xiv, 10, 16, 17, 21–22, 225
吸收，193
absorption of, 193
原子和，192
atoms and, 192
黑体辐射和，192
blackbody radiation and, 192
来自黑洞，242
from black holes, 242
bremsstrahlung emissions and, 192, 194
癌症和，193
cancer and, 193
创建于192 年
creation of, 192
定义，191
definition of, 191
从太空探测到，17-18、187-88、199、200-201
detected from space, 17–18, 187–88, 199, 200–201
能量，191-92
energy of, 191–92
通量（强度变化）为，212 –15
flux (varied intensity) of, 212–15
频率为191
frequency of, 191
轻盈，191-92
light and, 191–92
亮度为，246
luminosity of, 246
来自月球，193-94
from Moon, 193–94
来自太阳，192-93
from Sun, 192–93
来自超新星，223
from supernova, 223
synchrotron radiation from, 192
望远镜和，190
telescopes and, 190
杨，托马斯，94-95，154，269
Young, Thomas, 94–95, 154, 269
YouTube 、x、xii、164、170、225
YouTube, x, xii, 164, 170, 225
Z玻色子，18
Z bosons, 18
泽尔多维奇，雅科夫，253
Zel’dovich, Yakov, 253
零重力环境，47
zero-gravity environment, 47
关于作者
ABOUT THE AUTHORS
沃尔特·莱温出生于荷兰，并在那里长大。1965年，他获得代尔夫特理工大学物理学博士学位。1966年，他来到麻省理工学院担任博士后研究员。同年，他晋升为助理教授，并于1974年成为正教授。他是一位成就卓著的天体物理学家，也是X射线天文学的先驱，发表了超过450篇科学论文。莱温在麻省理工学院教授三门核心物理课程超过30年。这些课程广受欢迎，被录制成视频，并在麻省理工学院的开放课程平台、YouTube、iTunes U和Academic Earth等平台上迅速走红。每年，来自世界各地的超过一百万人观看这些视频。他的讲座广受好评，众多媒体都曾报道过，包括《纽约时报》、《波士顿环球报》、《国际先驱论坛报》、《卫报》、《华盛顿邮报》、《新闻周刊》和《美国新闻与世界报道》。他获得的荣誉和奖项包括：美国国家航空航天局杰出科学成就奖章（1978年）、亚历山大·冯·洪堡奖、古根海姆奖学金（1984年）、麻省理工学院科学委员会本科教学卓越奖（1984年）、麻省理工学院物理系W·布赫纳奖（1988年）、美国国家航空航天局脉冲星爆发发现团队成就奖（1997年）以及埃弗雷特·摩尔·贝克本科教学卓越纪念奖（2003年）。他于1993年当选为荷兰皇家艺术与科学院通讯院士和美国物理学会会士。
Walter Lewin was born and raised in the Netherlands. In 1965 he received his PhD in Physics from the University of Technology in Delft. He arrived at MIT in 1966 as a postdoctoral fellow. That same year he became an assistant professor and in 1974 was made full professor. He is a highly accomplished astrophysicist, a pioneer in X-ray astronomy, and has published more than four hundred and fifty scientific articles. Lewin taught the three physics core classes at MIT for more than thirty years. These lectures were so popular that they were videotaped and became hits on MIT’s OpenCourseWare, YouTube, iTunes U, and Academic Earth. More than a million people from all over the world watch these lectures yearly. Acclaim for his lectures has been featured in many media outlets, including the New York Times, Boston Globe, International Herald Tribune, Guardian, Washington Post, Newsweek, and U.S. News and World Report. His honors and awards include the NASA Exceptional Scientific Achievement Medal (1978), the Alexander von Humboldt Award, a Guggenheim Fellowship (1984), MIT’s Science Council Prize for Excellence in Undergraduate Teaching (1984), the W. Buechner Prize of the MIT Department of Physics (1988), the NASA Group Achievement Award for the Discovery of the Bursting Pulsar (1997), and the Everett Moore Baker Memorial Award for Excellence in Undergraduate Teaching (2003). He became a corresponding member of the Royal Netherlands Academy of Arts and Sciences and Fellow of the American Physical Society in 1993.
沃伦·戈德斯坦是哈特福德大学历史系教授兼系主任，曾荣获该校詹姆斯·E·和弗朗西丝·W·本特学术创新奖（2006年）。他毕生热爱物理学。作为一位著作颇丰且屡获殊荣的历史学家、散文家、记者和讲师，他之前的著作包括《全力以赴：早期棒球史》以及广受好评的传记《小威廉·斯隆·科芬：一位充满激情的人物》。他关于历史、教育、宗教、政治和体育的文章曾发表于《纽约时报》、《华盛顿邮报》、《高等教育纪事报》、《波士顿环球报》、《新闻日报》、《芝加哥论坛报》、《费城问询报》、《国家》、《基督教世纪》、《耶鲁校友杂志》、《泰晤士报文学副刊》和《赫芬顿邮报》。
Warren Goldstein is a professor of history and chair of the History Department at the University of Hartford, where he was the recipient of the James E. and Frances W. Bent Award for Scholarly Creativity (2006). He has a lifelong fascination with physics. A prolific and prizewinning historian, essayist, journalist, and lecturer, his prior books include Playing for Keeps: A History of Early Baseball, and the critically acclaimed biography William Sloane Coffin, Jr.: A Holy Impatience. His writing about history, education, religion, politics, and sports has appeared in the New York Times, Washington Post, Chronicle of Higher Education, Boston Globe, Newsday, Chicago Tribune, Philadelphia Inquirer, Nation, Christian Century, Yale Alumni Magazine, Times Literary Supplement, and Huffington Post.
*这种情况也发生在莉泽·迈特纳身上，她帮助发现了核裂变；罗莎琳德·富兰克林，她帮助发现了 DNA 的结构；还有乔斯林·贝尔，她发现了脉冲星，本应分享 1974 年诺贝尔奖，该奖项授予了她的导师安东尼·休伊什，以表彰他在发现脉冲星方面发挥的决定性作用。
* It happened to Lise Meitner, who helped discover nuclear fission; Rosalind Franklin, who helped discover the structure of DNA; and to Jocelyn Bell, who discovered pulsars and who should have shared in the 1974 Nobel Prize given to her supervisor, Antony Hewish, for “his decisive role in the discovery of pulsars.”
*英国皇家学会最近在网上发布了斯图克利手稿的数字图像，您可以在这里找到：http://royalsociety.org/turning-the-pages/。
* The Royal Society recently posted a digital image of Stukeley’s manuscript online, which you can find here: http://royalsociety.org/turning-the-pages/.
*如果你想在家使用这个公式，g取 9.8，h的单位是米；v的单位就是米/秒。如果h是 3 米（离地面 3 米），物体落地时的速度大约是 5.4 米/秒，也就是大约 12 英里/小时。
* If you want to use this equation at home, use 9.8 for g and give h in meters; v is then in meters per second. If h is 3 meters (above the floor), the object will hit the floor at about 5.4 meters per second which is about 12 miles per hour.
顺便一提，赤道上的重力加速度比两极低0.18%，因为地球并非完美球体。赤道上的物体比两极的物体距离地心远约20公里，因此赤道上的重力加速度g较小。9.82是平均值。
* This acceleration, by the way, is 0.18 percent lower at the equator than at the poles—because Earth is not a perfect sphere. Objects at the equator are about 20 kilometers farther away from the Earth’s center than objects at the poles, so at the equator g is lower. The 9.82 is an average value.
